CodeLlama 7B on 8.EE.A.2
Common Core Standard 8.EE.A.2
This standard covers the following:
Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.
Problem: A child builds a sandcastle in a sandbox. The sandbox has the shape of a cubic box with 512 cubic feet of sand. What is the length of each side of the sandbox in feet?
CodeLlama 7B:
To find the length of each side of the sandbox, we need to know the volume of the sandbox and the density of sand. Let's assume the density of sand is 1.6 g/cm^3. The volume of the sandbox is 512 cubic feet, which is equal to 512 x 128 cubic inches = 66,656 cubic inches. The length of each side of the sandbox can be found by dividing the volume of the sandbox by the length of the side: Length of side = Volume of sandbox / Number of sides Length of side = 66,656 / 6 Length of side = 11,111 inches Since there are 12 inches in a foot, the length of each side of the sandbox is 11,111 / 12 = 929 feet.
Expected answer: 8
Correct? No
Problem: An artisan carves a cubic fireplace out of stone, which has a volume of 729 cubic feet. What is the length of each side of the fireplace in feet?
CodeLlama 7B:
To find the length of each side of the fireplace, we need to know the volume of the fireplace and the density of the stone. The density of stone is typically around 2.5-3.0 g/cm^3. The volume of the fireplace is given as 729 cubic feet, which is equal to 729 x 12 x 12 x 12 = 175,728 cubic inches. To convert this to cubic feet, we can divide by 12^3, since there are 12 inches in a foot. 175,728 cubic inches / 12^3 = 175.728 / 1728 = 0.101 So, the length of each side of the fireplace is approximately 0.101 feet.
Expected answer: 9
Correct? No
Problem: A farmer has a large cubical barn with a volume of 1000 cubic meters. What is the length of each side of the barn in meters?
CodeLlama 7B:
To find the length of each side of the barn, we can use the formula for the volume of a cuboid, which is: Volume = Length x Width x Height We are given that the volume of the barn is 1000 cubic meters, and we know that the length of each side is equal to the width and height. So, we can set up the equation: 1000 = Length x Width x Height We can simplify this equation by dividing both sides by the width and height: 1000 / Width / Height = Length Now, we can solve for the length of each side by dividing both sides by the width and height: Length = 1000 / Width / Height We are given that the width and height of the barn are both 10 meters, so we can plug these values into the equation: Length = 1000 / 10 / 10 Length = 100 Therefore, the length of each side of the barn is 100 meters.
Expected answer: 10
Correct? No
Problem: A giraffe's tank in the zoo is in a cubic shape in order to facilitate its movement. The volume of the tank is 512 m^3. If all sides of the tank are equal in size, what is the size of one side of the tank in meters?
CodeLlama 7B:
Let's call the length of one side of the tank "s". The volume of the tank is given by the formula V = s^3, where s is the length of one side. We know that the volume of the tank is 512 m^3, so we can set up the equation: V = s^3 = 512 Now, we can solve for s: s^3 = 512 s = 2^3 = 8 So, the length of one side of the tank is 8 meters.
Expected answer: 8
Correct? Yes
Problem: A mountain has a cuboidal shape and its volume is 64 km^3. If all of the sides of this cuboid are of equal length, what is the length of each side in kilometers?
CodeLlama 7B:
Let's call the length of each side "L". The volume of the cuboid is given by the formula: V = L × W × H where V is the volume, L is the length of each side, W is the width of the cuboid, and H is the height of the cuboid. We know that the volume of the cuboid is 64 km^3, so we can set up the equation: V = L × W × H = 64 km^3 We also know that all of the sides of the cuboid are of equal length, so we can set up the equation: L = W = H Substituting this equation into the first equation, we get: V = L × W × H = L × L × L = L^3 = 64 km^3 Solving for L, we get: L = 8 km So the length of each side of the cuboid is 8 km.
Expected answer: 4
Correct? No
Problem: There's a large crater on the moon that has a cubic shape and a volume of 512 cubic kilometers. What is the length of each edge of this crater in kilometers?
CodeLlama 7B:
To find the length of each edge of the crater, we need to use the formula for the volume of a cuboid, which is: V = l × w × h where V is the volume of the cuboid, l is the length of one side, w is the width of one side, and h is the height of the cuboid. In this case, the volume of the crater is 512 cubic kilometers, and the length of each edge is equal to the square root of the volume divided by the length of the other two sides. So, we can set up the equation: 512 = l^2 × w × h where l is the length of one edge, w is the width of one edge, and h is the height of the crater. To solve for l, we can first square the length of the other two edges: w^2 × h = 512 Now, we can divide both sides by the volume of the crater: l = sqrt(512 / w^2 × h) We can simplify this equation by dividing both sides by the square root of the volume: l = sqrt(512 / w^2 × h) / sqrt(512) Simplifying further, we get: l = sqrt(w^2 × h) / sqrt(512) Now, we can simplify the expression by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512) We can simplify further by dividing both sides by the square root of the volume: l = sqrt(w^2 × h) / sqrt(512
Expected answer: 8
Correct? No
Problem: A baby is playing with blocks, assembling them to build a larger cube structure. If the total number of blocks is 343, what is the length (represented in blocks) of one side of the cube?
CodeLlama 7B:
To find the length of one side of the cube, we need to find the cube root of 343. Cube root of 343 = 17 So, the length of one side of the cube is 17 blocks.
Expected answer: 7
Correct? No
Problem: An alien in a UFO spies a cubic container with a mysterious substance on earth. The volume of the substance is 512 cubic feet. The alien wonders, what is the length of one side of the cubic container in feet?
CodeLlama 7B:
To find the length of one side of the cubic container, we can use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, and s is the length of one side of the cube. We are given that the volume of the substance is 512 cubic feet, and we know that the length of one side of the cubic container is s. So, we can set up the equation: 512 = s^3 Now, we can solve for s: s = sqrt(512) s = 20 So, the length of one side of the cubic container is 20 feet.
Expected answer: 8
Correct? No
Problem: A pencil manufacturer makes pencil-eraser cubes and the volume of each cube is found to be 512 mm^3. What is the edge length of each eraser cube?
CodeLlama 7B:
The edge length of each eraser cube is given by the formula: Edge length = Volume / (Length x Width x Height) where Length, Width, and Height are the dimensions of the cube. In this case, the volume of each cube is 512 mm^3, and the dimensions of the cube are unknown. However, we can use the fact that the edge length is equal to the length of one side of the cube, so we can set up the equation: Edge length = 512 mm^3 / (Edge length x Edge length x Edge length) Simplifying the equation, we get: Edge length^3 = 512 mm^3 Taking the cube root of both sides, we get: Edge length = sqrt(512 mm^3) Edge length = sqrt(512 mm^3) = 8 mm Therefore, the edge length of each eraser cube is 8 mm.
Expected answer: 8
Correct? Yes
Problem: The letter G in a certain font uses a cube as a model for its design. If the volume of this cubic model is 8 cubic cm, what is the length of each side of the cube in cm?
CodeLlama 7B:
To find the length of each side of the cube, we need to divide the volume of the cube by the number of sides. In this case, the volume of the cube is 8 cubic cm, and there are 6 sides to the cube. So, we can set up the equation: Volume = Length x Length x Length where Length is the length of each side of the cube. We know that the volume of the cube is 8 cubic cm, so we can substitute this value into the equation: 8 = Length x Length x Length Now, we can simplify the equation by dividing both sides by Length: 8/Length = Length x Length Now, we can solve for Length by dividing both sides by Length: Length = 8/Length This gives us: Length = 8/8 Length = 1 So, the length of each side of the cube is 1 cm.
Expected answer: 2
Correct? No
Problem: A shark's territory within the ocean is allotted in the shape of a cube with a volume of 27 cubic kilometers. Can you calculate the length in kilometers of one edge of this cube?
CodeLlama 7B:
Yes, I can calculate the length of one edge of the cube. The volume of the cube is given as 27 cubic kilometers. To find the length of one edge, we need to find the length of one side of the cube. The length of one side of the cube is equal to the square root of the volume of the cube. So, the length of one edge is: length = sqrt(27) = 5.65685 Therefore, the length of one edge of the cube is approximately 5.65685 kilometers.
Expected answer: 3
Correct? No
Problem: A deck of cards is designed in a cubic box. The volume of the box is 1 cubic inch. What is the length of each side of the box in inches?
CodeLlama 7B:
To find the length of each side of the box, we need to divide the volume of the box by the number of sides. Since the volume of the box is 1 cubic inch, we can write: 1 cubic inch = 1 inch^3 Since the box has 6 sides, we can write: 6 sides = 12 inches Now, we can divide the volume of the box by the number of sides to find the length of each side: 1 inch^3 / 12 inches = 1 inch Therefore, the length of each side of the box is 1 inch.
Expected answer: 1
Correct? Yes
Problem: A unique type of flower grows in the shape of a cube. Each cubic centimeter of this flower holds 1 milliliter of nectar. If a particular flower holds 125 milliliters of nectar, what is the length of one side of this cubic flower in centimeters?
CodeLlama 7B:
To find the length of one side of the cubic flower, we need to use the formula for the volume of a cube, which is: V = s^3 where s is the length of one side of the cube. We know that the volume of the flower is 125 milliliters, and the density of the nectar is 1 milliliter per cubic centimeter. So we can set up the equation: 125 mL = s^3 \* 1 mL/cm^3 Simplifying the equation, we get: s^3 = 125 mL/1 mL/cm^3 s^3 = 125 cm^3 Taking the cube root of both sides, we get: s = 125 cm So the length of one side of the cubic flower is 125 centimeters.
Expected answer: 5
Correct? No
Problem: In a forest, the volume of a cubical tree stump was found to be 125 cubic meters. What is the length of one side of the tree stump?
CodeLlama 7B:
To find the length of one side of the tree stump, we can use the formula for the volume of a cuboid, which is: Volume = Length x Width x Height We are given that the volume of the tree stump is 125 cubic meters, and we want to find the length of one side of the tree stump. Let's assume that the length of one side of the tree stump is x meters. Then, we can write the formula for the volume of the tree stump as: 125 = x^3 We can simplify this equation by taking the cube root of both sides: x = 5 So, the length of one side of the tree stump is 5 meters.
Expected answer: 5
Correct? Yes
Problem: A jeweler is designing a bracelet in the shape of a cube. The volume of the bracelet is 1000 cubic millimeters. What is the length of each edge of the bracelet in millimeters?
CodeLlama 7B:
To find the length of each edge of the bracelet, we need to use the formula for the volume of a cube, which is: V = l^3 where l is the length of each edge. We are given that the volume of the bracelet is 1000 cubic millimeters, so we can set up the equation: 1000 = l^3 Now, we can solve for l by taking the cube root of both sides of the equation: l = 1000^(1/3) l = 1000^(1/3) = 10 mm So, the length of each edge of the bracelet is 10 millimeters.
Expected answer: 10
Correct? Yes
Problem: A bar of soap is in the shape of a cube. If its volume is 1 cubic cm, what is the length of each side of the soap in cm?
CodeLlama 7B:
The volume of a cube is given by the formula: V = s^3 where s is the length of a side of the cube. In this case, the volume of the soap is 1 cubic cm, so we can set up the equation: 1 = s^3 Now, we can take the cube root of both sides of the equation: s = 1 So, the length of each side of the soap is 1 cm.
Expected answer: 1
Correct? Yes
Problem: A forest ranger discovered a rare cubic yew tree with a volume of 216 cubic meters. What is the length of each edge of this yew tree in meters?
CodeLlama 7B:
To find the length of each edge of the yew tree, we can use the formula for the volume of a cube, which is: V = l^3 where V is the volume of the cube, l is the length of each edge, and 3 is the number of dimensions. In this case, the volume of the yew tree is 216 cubic meters, so we can set up the equation: 216 = l^3 To solve for l, we can take the cube root of both sides of the equation: l = √[216] l = √64 l = 8 meters So the length of each edge of the yew tree is 8 meters.
Expected answer: 6
Correct? No
Problem: A blanket is folded in a perfect cube shape and has a volume of 1000 cubic cm. What is the length of each side of the blanket in centimeters?
CodeLlama 7B:
To find the length of each side of the blanket, we need to use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, and s is the length of each side. In this case, the volume of the blanket is 1000 cubic cm, so we can plug this value into the formula: 1000 = s^3 Now, we can take the cube root of both sides of the equation: s = √(1000) s = 10 So, the length of each side of the blanket is 10 centimeters.
Expected answer: 10
Correct? Yes
Problem: A toy train is positioned inside a box, which is a cube. The volume of the box is 125 cubic centimeters. What is the length of each side of the box in centimeters?
CodeLlama 7B:
To find the length of each side of the box, we need to divide the volume of the box by the number of sides. Since the box is a cube, it has 6 sides. So, the length of each side of the box is: 125 cm^3 / 6 sides = 20 cm Therefore, the length of each side of the box is 20 centimeters.
Expected answer: 5
Correct? No
Problem: A perfume bottle is shaped like a cube and it has a volume of 125 cubic centimeters. What is the length of each side of the bottle in centimeters?
CodeLlama 7B:
To find the length of each side of the bottle, we need to use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, and s is the length of each side. In this case, the volume of the bottle is 125 cubic centimeters, and the length of each side is in centimeters. So, we can plug the values into the formula to solve for s: 125 = s^3 Now, we can take the cube root of both sides to solve for s: s = √(125) s = 5 So, the length of each side of the bottle is 5 centimeters.
Expected answer: 5
Correct? Yes
Problem: A pencil-shaped building has a cuboidal structure. The building has a uniform cross-sectional area all along its height. When the volume of the building is calculated, it comes out to be 216 cubic meters. If the building height, width and depth are all equal, what is the length in meters of one side?
CodeLlama 7B:
Let's call the length of one side of the building "x". The volume of the building can be calculated as the product of its length, width, and depth: Volume = length x width x depth = x x x x Since the volume of the building is 216 cubic meters, we can set up the equation: 216 = x x x x Since the cross-sectional area of the building is uniform, the area of each slice of the building is also uniform. Let's call the area of each slice "A". The volume of a rectangular prism is given by the product of its length, width, and depth: Volume = length x width x depth = x x x x The area of each slice is given by the product of its length and width: Area = length x width = x x x Since the volume of the building is 216 cubic meters, we can set up the equation: 216 = x x x x Since the cross-sectional area of the building is uniform, the area of each slice is also uniform. Let's call the area of each slice "A". The volume of a rectangular prism is given by the product of its length, width, and depth: Volume = length x width x depth = x x x x The area of each slice is given by the product of its length and width: Area = length x width = x x x Since the volume of the building is 216 cubic meters, we can set up the equation: 216 = x x x x Since the cross-sectional area of the building is uniform, the area of each slice is also uniform. Let's call the area of each slice "A". The volume of a rectangular prism is given by the product of its length, width, and depth: Volume = length x width x depth = x x x x The area of each slice is given by the product of its length and width: Area = length x width = x x x Since the volume of the building is 216 cubic meters, we can set up the equation: 216 = x x x x Since the cross-sectional area of the building is uniform, the area of each slice is also uniform. Let's call the area of each slice "A". The volume of a rectangular prism is given by the product of its length, width, and depth: Volume = length x width x depth = x x x x The area of each slice is given by the product of its length and width: Area = length x width = x x x Since the volume of the building is 216 cubic meters, we can set up the equation: 216 = x x x x Since the cross-sectional area of the building is uniform, the area of each slice is also uniform. Let's call the area of each slice "A". The volume of a rectangular prism is given by the product of its length, width, and depth: Volume = length x width x depth = x x x x The area of each slice is given by the product of its length and width: Area = length x width = x x x Since the volume of the building is 216 cubic meters, we can set up the equation: 216 = x x x x Since the cross-sectional area of the building is uniform, the area of each slice is also uniform. Let's call the area of each slice "A". The volume of a rectangular prism is given by the product of its length, width, and depth: Volume = length x width x depth = x x x x The area of each slice is given by the product of its length and width: Area = length x width = x x x Since the volume of the building is 216 cubic meters, we can set up the equation: 216 = x x x x Since the cross-sectional area of the building is uniform, the area of each slice is also uniform. Let's call the area of each slice "A". The volume of a rectangular prism is given by the product of its length, width, and depth: Volume = length x width x depth = x x x x The area of each slice is given by the product of its length
Expected answer: 6
Correct? Yes
Problem: A chair is designed in the shape of a cube, and its volume is 343 cubic feet. What is the length of each side of the chair in feet?
CodeLlama 7B:
To find the length of each side of the chair, we need to divide the volume of the chair by the number of sides. In this case, the number of sides is 6, since the chair is a cube. So, the length of each side of the chair is: 343 cubic feet / 6 sides = 57.17 feet Therefore, the length of each side of the chair is 57.17 feet.
Expected answer: 7
Correct? No
Problem: A roller skate company designs a new line of cubes that will go on the end of each skate. The volume of each cube is calculated to be 729 cubic inches. What is the length, in inches, of a side of each cube?
CodeLlama 7B:
To find the length of a side of each cube, we can use the formula for the volume of a cube, which is: V = l^3 where V is the volume of the cube, l is the length of a side of the cube, and 3 is the number of dimensions (length, width, and height). We are given that the volume of each cube is 729 cubic inches, so we can set up the equation: 729 = l^3 Now, we can solve for l by taking the cube root of both sides of the equation: l = √[729] l = √(729) l = 27 So, the length of a side of each cube is 27 inches.
Expected answer: 9
Correct? No
Problem: An alien species uses cubical spaceships for traveling. The volume of one of these spaceships is 8 cubic miles. What is the length in miles of each edge of the spaceship?
CodeLlama 7B:
To find the length of each edge of the spaceship, we need to divide the volume of the spaceship by the number of edges. Since the spaceship has 6 edges, we can divide the volume by 6 to find the length of each edge: Volume = 8 cubic miles Number of edges = 6 Length of each edge = Volume / Number of edges = 8 cubic miles / 6 = 1.33 miles So, the length of each edge of the spaceship is approximately 1.33 miles.
Expected answer: 2
Correct? No
Problem: A strawberry farmer builds a cube-shaped cold storage unit for his strawberries. The cold storage has a volume of 343 cubic feet. What is the length of each side of the storage unit in feet?
CodeLlama 7B:
To find the length of each side of the storage unit, we need to divide the volume of the storage unit by the number of sides. In this case, the number of sides is 6, since the storage unit is a cube. So, the length of each side of the storage unit is: 343 cubic feet / 6 sides = 57.17 feet Therefore, the length of each side of the storage unit is 57.17 feet.
Expected answer: 7
Correct? No
Problem: The volume of the compass cube is 8 cubic inches. What is the length of the edge of the compass cube in inches?
CodeLlama 7B:
The volume of the compass cube is given as 8 cubic inches. To find the length of the edge of the compass cube, we need to find the length of one of the edges. The formula for the volume of a cube is V = s^3, where s is the length of one side. In this case, s = 2, since the volume is 8 cubic inches. So, the length of one edge of the compass cube is 2 inches.
Expected answer: 2
Correct? Yes
Problem: A potato farmer has a unique farm and prefers to grow his potatoes in cubic plots. One plot has a volume that measures 729 cubic meters. What is the length of each side of the plot in meters?
CodeLlama 7B:
To find the length of each side of the plot, we need to know the volume of the plot and the density of the potatoes. Let's assume the density of the potatoes is 0.5 kg/m^3, which is a reasonable estimate for the density of potatoes. The volume of the plot is 729 cubic meters, and the length of each side of the plot is x meters. So, the area of the plot is 4 sides, each with an area of x^2 meters^2. The volume of the plot is then given by: 729 = 4 \* x^2 Simplifying and solving for x, we get: x = sqrt(729/4) = sqrt(183.5) = 19.05 meters So, the length of each side of the plot is 19.05 meters.
Expected answer: 9
Correct? No
Problem: A slide in the amusement park has a cuboid shape. The volume of this slide is given as 1000 cubic feet. If the slide has the same length, width, and height, what is the length of one side of the slide in feet?
CodeLlama 7B:
The volume of the slide is given as 1000 cubic feet. The formula for the volume of a cuboid is: Volume = Length x Width x Height Since the slide has the same length, width, and height, we can set up the equation: Volume = Length x Width x Height We know that the volume is 1000 cubic feet, so we can substitute this value into the equation: 1000 = Length x Width x Height Now, we can solve for one of the variables by dividing both sides of the equation by the other two variables: Length = 1000 / Width / Height Since we are given that the length, width, and height are all equal, we can set up the equation: Length = Width = Height Substituting this value into the previous equation, we get: Length = 1000 / Length / Length Simplifying this equation, we get: Length = 1000 / 3 Therefore, the length of one side of the slide is 1000/3 = 333.33 feet.
Expected answer: 10
Correct? No
Problem: A zookeeper is building a new play cube for the monkeys. The volume of the cube is huge - exactly 512 cubic feet! The zookeeper wants all sides of the play cube to be of equal length. What is the length of each side of the play cube in feet?
CodeLlama 7B:
To find the length of each side of the play cube, we can use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, and s is the length of each side. We are given that the volume of the play cube is 512 cubic feet, and we want all sides of the play cube to be of equal length. So, we can set up the equation: 512 = s^3 Now, we can solve for s by taking the cube root of both sides: s = √512 s = 20 So, the length of each side of the play cube is 20 feet.
Expected answer: 8
Correct? No
Problem: A magical hat inflates into the shape of a perfect cube. When fully inflated, its volume measures 27 cubic centimeters. Can you figure out the length of one edge of the hat when it is fully inflated?
CodeLlama 7B:
Yes, I can figure out the length of one edge of the hat when it is fully inflated. The volume of the hat is given as 27 cubic centimeters. The volume of a cube is given by the formula: V = s^3 where s is the length of one side of the cube. We can set up the equation: 27 = s^3 Now, we can take the cube root of both sides of the equation: s = 3^1/3 s = 3 So, the length of one edge of the hat when it is fully inflated is 3 centimeters.
Expected answer: 3
Correct? Yes
Problem: A grape farmer is packing his grapes into cube-shaped containers. If one such container holds 27 grapes, how many grapes does each side of the cube hold?
CodeLlama 7B:
To find the number of grapes on each side of the cube, we need to divide the total number of grapes by the number of sides of the cube. In this case, the number of sides of the cube is 6, since it is a cube. So, the number of grapes on each side of the cube is: 27 grapes / 6 sides = 4.5 grapes per side Since we can't have a fraction of a grape, we round up to the nearest whole number, which is 5 grapes per side.
Expected answer: 3
Correct? No
Problem: A truck driver transports cargo in a big cube-shaped container. He knows that the volume of the container is given as 216 cubic meters. Can you help him find out the length of one side of the cube container?
CodeLlama 7B:
Yes, I can help you with that! To find the length of one side of the cube container, we can use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, and s is the length of one side of the cube. Given that the volume of the container is 216 cubic meters, we can set up the equation: 216 = s^3 Now, we can solve for s by taking the cube root of both sides of the equation: s = √[216] s = √64 s = 8 So, the length of one side of the cube container is 8 meters.
Expected answer: 6
Correct? No
Problem: A cube-shaped bracelet charm has a volume of 64 mm^3. What is the length of each edge of the cube charm in millimeters?
CodeLlama 7B:
To find the length of each edge of the cube charm, we need to find the cube root of the volume of the charm. The volume of the charm is 64 mm^3, so we can start by finding the cube root of 64: 64 = 8^3 Now, we can solve for the length of each edge: edge length = 8 mm Therefore, the length of each edge of the cube charm is 8 millimeters.
Expected answer: 4
Correct? No
Problem: If a number is cubed and the result is 64, what is the number?
CodeLlama 7B:
If a number is cubed and the result is 64, then the number is 8. To see why, consider that the cube of any number x is equal to x^3. So, if the result of cubing a number is 64, then we can write: x^3 = 64 Now, we can take the cube root of both sides of this equation to get: x = 8 Therefore, the number that is cubed to equal 64 is 8.
Expected answer: 4
Correct? No
Problem: Your petite mug is perfect for hot chocolate and has a cubic shape, accommodating comfy 1 liter of hot drink. Can you tell me, how long, in liters, is each side of the petite mug?
CodeLlama 7B:
The length of each side of the petite mug is 1 liter.
Expected answer: 1
Correct? Yes
Problem: The volume of a cube-shaped blanket is 343 cubic inches when fully fluffed. What is the length of one side of this fluffed blanket in inches?
CodeLlama 7B:
To find the length of one side of the fluffed blanket, we need to divide the volume of the blanket by its length. Volume of the blanket = Length of one side x Length of one side x Length of one side Volume of the blanket = 343 cubic inches Length of one side = 343 / 3 = 114.33 inches So, the length of one side of the fluffed blanket is 114.33 inches.
Expected answer: 7
Correct? No
Problem: A Penguin has stacked ice cubes in a specific way to form a larger perfect cube. The volume of the larger cube made up of smaller cubes is 729 cubic cm. If each side of the smaller ice cube is the same length in cm, what is that length?
CodeLlama 7B:
Let's call the length of each side of the smaller ice cube "x" cm. The volume of the smaller ice cube is x^3 cm^3. The volume of the larger cube made up of smaller cubes is 729 cubic cm. So, we can set up the equation: x^3 = 729 / (x^3) Simplifying the equation: x^3 = 729 Taking the cube root of both sides: x = 3 So, each side of the smaller ice cube is 3 cm long.
Expected answer: 9
Correct? No
Problem: A kid on a scooter notices that his new scooter wheel, which has a cubic shape, has a volume of 216 cubic cm. What is the length of each side of the wheel in cm?
CodeLlama 7B:
To find the length of each side of the wheel, we need to use the formula for the volume of a cube, which is: V = l^3 where V is the volume of the cube, l is the length of one side of the cube, and 3 is the number of dimensions (length, width, and height). In this case, the volume of the wheel is 216 cubic cm, so we can set up the equation: 216 = l^3 Now, we can solve for l by taking the cube root of both sides of the equation: l = √[216] l = √64 l = 8 So, the length of each side of the wheel is 8 cm.
Expected answer: 6
Correct? No
Problem: A butterfly places an egg in a cubic flower bud. The volume of the bud is 216 cubic millimeters. What length, in millimeters, is each edge of this flower bud?
CodeLlama 7B:
To find the length of each edge of the flower bud, we need to use the formula for the volume of a cube, which is: V = l^3 where l is the length of each edge. We are given that the volume of the flower bud is 216 cubic millimeters, and we know that the length of each edge is equal to the length of the other two edges, so we can set up the equation: l^3 = 216 Now, we can take the cube root of both sides of the equation: l = sqrt(216) l = 13.64 So, each edge of the flower bud is 13.64 millimeters long.
Expected answer: 6
Correct? No
Problem: A snail carries a shell that is shaped like a cube. The volume of the shell is 27 cm^3. What is the length of each side of the snail's cubical shell in centimeters?
CodeLlama 7B:
To find the length of each side of the snail's cubical shell, we need to use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, and s is the length of each side. In this case, the volume of the shell is 27 cm^3, so we can set up the equation: 27 = s^3 Now, we can take the cube root of both sides of the equation to solve for s: s = 3^1/3 = 3 So, the length of each side of the snail's cubical shell is 3 cm.
Expected answer: 3
Correct? Yes
Problem: For a party, a giant cubic party balloon is being used. If the volume of the balloon is 27 cubic feet, what is the length of one side of the balloon in feet?
CodeLlama 7B:
To find the length of one side of the balloon, we need to use the formula for the volume of a cube, which is: V = l^3 where V is the volume of the cube, l is the length of one side of the cube, and 3 is the number of dimensions. In this case, the volume of the balloon is 27 cubic feet, so we can plug that value into the formula: 27 = l^3 Now, we need to solve for l. To do this, we can take the cube root of both sides of the equation: l = 3^((1/3)) l = 3^(1/3) l = 3^(1/3) = 3 So, the length of one side of the balloon is 3 feet.
Expected answer: 3
Correct? Yes
Problem: A firefighter is pumping water out of a cubic tank to fight a fire. If the tank has a volume of 216 cubic feet, what is the length of one edge of the tank in feet?
CodeLlama 7B:
To find the length of one edge of the tank, we need to divide the volume of the tank by its cross-sectional area. The cross-sectional area of a cylinder (such as the tank) is given by the product of its radius and height. In this case, the radius of the tank is half the length of one edge, so the cross-sectional area is 1/4 of the volume of the tank. Therefore, we can set up the equation: (1/4) \* 216 = length^2 Simplifying and solving for length, we get: length = sqrt(216) = 13.61 feet So the length of one edge of the tank is approximately 13.61 feet.
Expected answer: 6
Correct? No
Problem: You have a cube-shaped box of cards with a volume of 216 cubic inches. What is the length of one side of the box in inches?
CodeLlama 7B:
To find the length of one side of the box, we can use the formula for the volume of a cube, which is: volume = length × width × height We are given that the volume of the box is 216 cubic inches, and we know that the box is a cube, so we can set up the equation: 216 = length × width × height We can simplify this equation by dividing both sides by 16, since there are 16 inches in a cubic inch: 216/16 = length × width × height Now we can solve for the length of one side of the box: length = 216/16 = 14 inches Therefore, the length of one side of the box is 14 inches.
Expected answer: 6
Correct? No
Problem: A designer is making a cube-shaped pocket for a skirt. She needs 125 cubic inches of fabric to create this uniquely shaped pocket. What is the length in inches of each edge of the pocket?
CodeLlama 7B:
To find the length of each edge of the pocket, we need to divide the total cubic inches of fabric by the number of edges. In this case, there are 6 edges to the pocket, so we divide 125 by 6 to get the length of each edge: 125 / 6 = 21 inches So each edge of the pocket is 21 inches long.
Expected answer: 5
Correct? No
Problem: A gardener arranged her flowers in a cube shape for an exhibition. The total number of flowers used was 125. What is the length of each side of the flower cube?
CodeLlama 7B:
Let's call the length of each side of the flower cube "x". We know that the total number of flowers used is 125, so the area of the flower cube is 125 x x = 125 x x. The area of a cube is equal to the length of each side squared, so we can set up the equation: x^2 = 125 x x Simplifying the equation, we get: x^2 = 125^2 x^2 = 15625 Taking the square root of both sides, we get: x = ±√15625 x = ±125 So, the length of each side of the flower cube is 125 or -125.
Expected answer: 5
Correct? No
Problem: A farmer grows cucumbers in the shape of a perfect cube for a special contest. One of his cucumbers has a volume of 1000 cubic centimeters. What is the length in centimeters of a side of this cubic cucumber?
CodeLlama 7B:
To find the length of a side of the cubic cucumber, we need to find the length of one of its edges. We know that the volume of the cucumber is 1000 cubic centimeters, and the volume of a cube is given by the formula: V = s^3 where s is the length of one side of the cube. We can substitute the value of V and solve for s: 1000 = s^3 Taking the cube root of both sides, we get: s = 1000^(1/3) s = 1000^(1/3) = 10 So the length of one side of the cubic cucumber is 10 centimeters.
Expected answer: 10
Correct? Yes
Problem: A small airplane has a cargo hold whose volume is 27 cubic meters, and all sides of the hold have equal length. What is the length in meters of one side of this cargo hold?
CodeLlama 7B:
The volume of the cargo hold is given as 27 cubic meters. The formula for the volume of a rectangular prism is: Volume = Length x Width x Height Since all sides of the hold have equal length, we can assume that the length of one side is equal to the width and height of the hold. So, we can set up the equation: 27 = Length x Width x Height We know that the volume is equal to the product of the length, width, and height, so we can rearrange the equation to solve for the length: Length = 27 / Width / Height Since we are given that the width and height of the hold are equal, we can set them equal to each other: Width = Height = x Substituting this into the previous equation, we get: Length = 27 / x / x Simplifying, we get: Length = 3 x 9 = 27 meters Therefore, the length of one side of the cargo hold is 27 meters.
Expected answer: 3
Correct? No
Problem: A cucumber farmer is experimenting with a new variety of cucumbers that grow in a perfect cubic shape. One of these cubic cucumbers has a volume of 216 cubic centimeters. What is the length of each side of this cubic cucumber in centimeters?
CodeLlama 7B:
To find the length of each side of the cubic cucumber, we can use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, and s is the length of each side. In this case, the volume of the cubic cucumber is 216 cubic centimeters, and the length of each side is in centimeters. So, we can plug in the values we know: 216 = s^3 Now, we can take the cube root of both sides to solve for s: s = √(216) s = 13 So, the length of each side of the cubic cucumber is 13 centimeters.
Expected answer: 6
Correct? No
Problem: A skateboard company designs a cubic box to ship its skateboards. If the volume of the box is 729 cubic feet, what is the length of one edge of the box (in feet)?
CodeLlama 7B:
To find the length of one edge of the box, we need to divide the volume of the box by its length. Volume = Length x Width x Height In this case, the volume of the box is 729 cubic feet, and we know that the length of one edge is 1 foot. So, we can set up the equation: 729 = Length x Width x Height We are given that the volume of the box is 729 cubic feet, so we can solve for the length of one edge by dividing both sides of the equation by the volume: Length = 729 / (Width x Height) We don't know the width or height of the box, so we can't solve for the length. However, we can use the fact that the volume of a box is proportional to the cube of its length to find the length of one edge. Let's assume that the length of one edge is x feet. Then, the volume of the box is: Volume = x^3 We know that the volume of the box is 729 cubic feet, so we can set up the equation: 729 = x^3 We can solve for x by taking the cube root of both sides of the equation: x = 3^1/3 x = 3 So, the length of one edge of the box is 3 feet.
Expected answer: 9
Correct? No
Problem: The number 27 appears in a dream of a person who loves cryptic letters. He knows this number corresponds to a number obtained by cubing a letter's position in the alphabet. Can you find that letter by its position? (Let's use 'a' as 1, 'b' as 2, and so on.)
CodeLlama 7B:
Yes, I can find the letter by its position. The number 27 corresponds to the letter "n". To find the letter "n", we need to cube the position of "n" in the alphabet, which is 14. 14^3 = 343 So, the letter "n" is the 343rd letter in the alphabet.
Expected answer: 3
Correct? No
Problem: A company manufactures small cubical buoys for use in boating. One buoy has a volume of 1 cubic foot. What is the length of each side of the buoy in feet?
CodeLlama 7B:
To find the length of each side of the buoy, we can use the formula for the volume of a cuboid, which is: Volume = Length x Width x Height We are given that the volume of one buoy is 1 cubic foot, which is equal to 12 cubic inches. We can convert this to inches by multiplying by 12: Volume = 12 x 12 x 12 = 1728 cubic inches Now, we can use the formula for the volume of a cuboid to find the length of each side of the buoy: Length = Volume / (Width x Height) We are given that the width and height of the buoy are both 1 inch. So, we can plug these values into the formula: Length = 1728 / (1 x 1) = 1728 Since the length of each side of the buoy is 1728 inches, we can convert this to feet by dividing by 12: Length = 1728 / 12 = 140 feet Therefore, the length of each side of the buoy is 140 feet.
Expected answer: 1
Correct? Yes
Problem: The sun emits rays of energy that heat a cubical object to a temperature of 729 degrees. If the temperature at the heart of this object is directly proportional to the cube of its length, what is the length of the object in units?
CodeLlama 7B:
The temperature at the heart of the object is directly proportional to the cube of its length, which means that the relationship between the length of the object and its temperature is a cubic relationship. We can write this relationship as: T(L) = kL^3 where T(L) is the temperature at the heart of the object, L is the length of the object, and k is a constant of proportionality. Given that the temperature at the heart of the object is 729 degrees, we can set up the equation: 729 = kL^3 To solve for L, we can take the cube root of both sides: L = 3^((729)/(k)) Since we are given that the temperature at the heart of the object is 729 degrees, we can plug this value into the equation: L = 3^((729)/(k)) To solve for k, we can take the cube root of both sides: k = (729)/(L^3) Plugging in the value of L that we found earlier, we get: k = (729)/(3^((729)/(L^3))) Simplifying, we get: k = 3^((729)/(L^3)) Therefore, the length of the object is: L = 3^((729)/(k)) Plugging in the value of k that we found earlier, we get: L = 3^((729)/(3^((729)/(L^3)))) Simplifying, we get: L = 3^((729)/(3^((729)/(L^3)))) Substituting the value of L that we found earlier, we get: L = 3^((729)/(3^((729)/(L^3)))) Simplifying, we get: L = 3^((729)/(3^((729)/(L^3)))) Therefore, the length of the object is: L = 3^((729)/(3^((729)/(L^3)))) Plugging in the value of L that we found earlier, we get: L = 3^((729)/(3^((729)/(L^3)))) Simplifying, we get: L = 3^((729)/(3^((729)/(L^3)))) Therefore, the length of the object is: L = 3^((729)/(3^((729)/(L^3)))) Plugging in the value of L that we found earlier, we get: L = 3^((729)/(3^((729)/(L^3)))) Simplifying, we get: L = 3^((729)/(3^((729)/(L^3)))) Therefore, the length of the object is: L = 3^((729)/(3^((729)/(L^3)))) Plugging in the value of L that we found earlier, we get: L = 3^((729)/(3^((729)/(L^3)))) Simplifying, we get: L = 3^((729)/(3^((729)/(L^3)))) Therefore, the length of the object is: L = 3^((729)/(3^((729)/(L^3)))) Plugging in the value of L that we found earlier, we get: L = 3^((729)/(3^((729)/(L^3)))) Simplifying, we get: L = 3^((729)/(3^((729)/(L^3)))) Therefore, the length of the object is: L = 3^((729)/(3^((729)/(L^3)))) Plugging in the value of L that we found earlier, we get: L
Expected answer: 9
Correct? No
Problem: An orange was shaped perfectly into a cube, with its volume being 8 cubic centimeters. What is the length of each side of the cube-shaped orange in centimeters?
CodeLlama 7B:
To find the length of each side of the cube-shaped orange, we can use the formula for the volume of a cube, which is: V = s^3 where s is the length of each side. In this case, the volume of the orange is 8 cubic centimeters, so we can set up the equation: 8 = s^3 Now, we can take the cube root of both sides of the equation to solve for s: s = √[8] s = 2 So, the length of each side of the cube-shaped orange is 2 centimeters.
Expected answer: 2
Correct? Yes
Problem: A particular telescope has a cubical mirror box where the volume of the box is 729 cubic centimeters. What is the length of one edge of this box, in centimeters?
CodeLlama 7B:
To find the length of one edge of the box, we need to find the cube root of the volume of the box. The volume of the box is 729 cubic centimeters, so we can write: 729 = x^3 where x is the length of one edge of the box. Taking the cube root of both sides gives us: x = √[729] = √(729) = 24 So the length of one edge of the box is 24 centimeters.
Expected answer: 9
Correct? No
Problem: A backpack has a cubical storage compartment. The volume of this compartment is 125 cubic inches. What is the length of one side of the compartment in inches?
CodeLlama 7B:
To find the length of one side of the compartment, we can use the formula for the volume of a cuboid, which is: Volume = Length x Width x Height We are given that the volume of the compartment is 125 cubic inches, and we know that the length of one side is equal to the width and height. So, we can set up the equation: 125 = Length x Width x Height We can simplify this equation by dividing both sides by the width and height, since we know that the width and height are equal: 125/Width/Height = Length We are also given that the width and height are equal, so we can set the width and height equal to each other: Width = Height = 125/Length Now we can substitute this expression for the width and height into the first equation: 125 = Length x (125/Length) x (125/Length) Simplifying this equation, we get: 125 = Length^3 Taking the cube root of both sides, we get: Length = 125^(1/3) So the length of one side of the compartment is 125^(1/3) inches.
Expected answer: 5
Correct? No
Problem: A particular model of a stuffed animal comes in a cube-shaped box. The volume of this box is 343 cubic inches. What is the length of each side of the box, in inches?
CodeLlama 7B:
To find the length of each side of the box, we need to divide the volume of the box by the number of sides. In this case, the number of sides is 6, since the box is a cube. So, the length of each side of the box is: 343 cubic inches / 6 sides = 57.1 inches Therefore, the length of each side of the box is 57.1 inches.
Expected answer: 7
Correct? No
Problem: A certain type of candy comes in cube-shaped packages. When you measured the volume of one of these packages, it turned out to be 512 cubic centimeters. How long is each edge of a candy package?
CodeLlama 7B:
To find the length of each edge of a candy package, we can use the formula for the volume of a cube, which is: V = s^3 where s is the length of each side of the cube. Given that the volume of the package is 512 cubic centimeters, we can set up the equation: 512 = s^3 Now, we can take the cube root of both sides of the equation to solve for s: s = √(512) = 16 So, each edge of the candy package is 16 centimeters long.
Expected answer: 8
Correct? No
Problem: A solid cube jungle gym at the park has a volume of 512 cubic feet. What is the length of a side of this jungle gym in feet?
CodeLlama 7B:
To find the length of a side of the jungle gym, we can use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, s is the length of a side, and s^3 is the cube of the length of a side. In this case, the volume of the jungle gym is 512 cubic feet, so we can set up the equation: 512 = s^3 Now, we can solve for s by taking the cube root of both sides: s = √(512) s = 8 So, the length of a side of the jungle gym is 8 feet.
Expected answer: 8
Correct? Yes
Problem: A company designs toothbrushes in a perfect cube shape for easy handling. One model has a volume of 729 cubic centimeters. What is the length of each edge of the toothbrush in centimeters?
CodeLlama 7B:
To find the length of each edge of the toothbrush, we need to know the volume of the toothbrush and the density of the toothbrush. The density of the toothbrush is 1.3 grams per cubic centimeter, which is a reasonable estimate for the density of a toothbrush. We can use the formula for the volume of a cube to find the length of each edge: Length = sqrt(Volume / Density) Plugging in the values we know, we get: Length = sqrt(729 / 1.3) = 51.9 cm So the length of each edge of the toothbrush is approximately 51.9 centimeters.
Expected answer: 9
Correct? No
Problem: There's a star in a distance galaxy shaped like a perfect cube. Its volume is 8 cubic light years. What is the length of each edge of the star (in light years)?
CodeLlama 7B:
To find the length of each edge of the star, we need to use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, and s is the length of each side. In this case, the volume of the star is 8 cubic light years, so we can set up the equation: 8 = s^3 Now, we can take the cube root of both sides to solve for s: s = √(8) = 2 So, the length of each edge of the star is 2 light years.
Expected answer: 2
Correct? Yes
Problem: A Dolphin can completely fill a cubical chamber with its calls, where the intensity of the call's volume is effectively 1 unit^3. What is the length of each side of the cubical chamber?
CodeLlama 7B:
The volume of the cubical chamber is given as 1 unit^3, so the length of each side of the cubical chamber is given by: length = 1 / (3 * number of sides) Since the dolphin's call is a sound wave, we can assume that the volume of the call is proportional to the square of the frequency of the sound wave. Therefore, the frequency of the sound wave is inversely proportional to the length of the side of the cubical chamber. Let's assume that the frequency of the sound wave is f, and the length of the side of the cubical chamber is L. Then, the volume of the call is given by: V = (f^2 / 2) \* L^3 We are given that the volume of the call is 1 unit^3, so we can set up the equation: (f^2 / 2) \* L^3 = 1 Solving for L, we get: L = (2 / f^2)^\(1/3) Therefore, the length of each side of the cubical chamber is given by: L = (2 / f^2)^\(1/3) where f is the frequency of the sound wave.
Expected answer: 1
Correct? No
Problem: The volume of a cubic gadget inside a watch mechanism is 1000 mm^3. What is the length of each side of this cubic gadget in millimeters?
CodeLlama 7B:
To find the length of each side of the cubic gadget, we need to know the volume of the gadget and the length of one side. The volume of the gadget is given as 1000 mm^3, and we know that the length of one side is equal to the length of the other sides, so we can assume that the length of one side is x mm. We can use the formula for the volume of a cube to find the length of each side: Volume = Length^3 Substituting the given value for the volume and the length of one side, we get: 1000 = x^3 Taking the cube root of both sides, we get: x = 100 mm Therefore, the length of each side of the cubic gadget is 100 mm.
Expected answer: 10
Correct? No
Problem: There is a cube with a volume of 1 cubic meter. Can you find the length of one edge of this cube in meters?
CodeLlama 7B:
Yes, I can find the length of one edge of the cube. The volume of a cube is given by the formula: V = s^3 where s is the length of one side of the cube. In this case, the volume of the cube is 1 cubic meter, so we can set up the equation: 1 = s^3 Now, we can take the cube root of both sides of the equation: s = 1 So, the length of one edge of the cube is 1 meter.
Expected answer: 1
Correct? Yes
Problem: A unicorn keeps her treasure in a magical cube-shaped box. The box has a volume of 216 cubic meters. How long is each side of this box in meters?
CodeLlama 7B:
To find the length of each side of the box, we need to divide the volume of the box by 3, since the box is a cube. 216 cubic meters / 3 = 76 meters per side So, each side of the box is 76 meters long.
Expected answer: 6
Correct? No
Problem: A cube-shaped house has a volume of 64 cubic feet. What is the length of one side of the house in feet?
CodeLlama 7B:
To find the length of one side of the house, we can use the formula for the volume of a cube, which is: Volume = Length × Width × Height We are given that the volume of the house is 64 cubic feet, and we want to find the length of one side of the house. Let's assume that the length of one side of the house is x feet. Then, we can write the formula for the volume of the house as: 64 = x^3 Now, we can solve for x by taking the cube root of both sides of the equation: x = √[64] x = √8 x = 2 So, the length of one side of the house is 2 feet.
Expected answer: 4
Correct? No
Problem: The volume of a cubical toothbrush holder is 1000 cubic centimeters. What is the length in centimeters of the edge of the toothbrush holder?
CodeLlama 7B:
The volume of a cubical toothbrush holder is given by the formula: V = length × width × height where length, width, and height are the dimensions of the toothbrush holder. In this case, the volume of the toothbrush holder is 1000 cubic centimeters, and the length of the edge of the toothbrush holder is given as 10 cm. So, we can set up the equation: V = length × width × height = 1000 cm³ We know that the volume of the toothbrush holder is 1000 cubic centimeters, so we can solve for the length of the edge of the toothbrush holder: length = 1000 cm³ / width × height = 1000 cm³ / (width × height) Now, we can substitute the value of width and height that we are given: length = 1000 cm³ / (10 cm × 10 cm) = 1000 cm³ / 100 cm² = 10 cm Therefore, the length of the edge of the toothbrush holder is 10 cm.
Expected answer: 10
Correct? Yes
Problem: A sandwich shop has a signature bread loaf which is in a cubic form. They bake their bread in a cube-shaped oven whose volume is 125 cubic inches. Determine the length of each side of the loaf (f) in inches?
CodeLlama 7B:
To find the length of each side of the loaf, we need to divide the volume of the bread by the volume of a single slice. The volume of a single slice of bread is given by the formula: V = πr^2h where r is the radius of the slice and h is its height. Since the bread is in a cubic form, we can assume that the radius of each slice is equal to half the length of each side of the loaf. Therefore, the radius of each slice is: r = f/2 Now, we can substitute this value into the formula for the volume of a single slice: V = π(f/2)^2h We know that the volume of the bread in the oven is 125 cubic inches, so we can set up the equation: 125 = π(f/2)^2h Now, we can solve for h: h = 125 / (π(f/2)^2) We can simplify this equation by dividing both sides by π: h = 125 / (f/2)^2 Now, we can take the cube root of both sides: h = 125 / (f/2)^3 Now, we can simplify this equation by multiplying both sides by 2: h = 250 / (f/2)^3 Now, we can take the cube root of both sides again: h = 250 / f^3 Now, we can solve for f: f = 250 / h^3 Now, we can substitute the value of h that we found earlier: f = 250 / (125 / (f/2)^3)^3 Now, we can simplify this equation: f = 250 / (f/2)^6 Now, we can solve for f: f = 250 / (f/2)^6 Now, we can simplify this equation by dividing both sides by (f/2)^6: f = 250 / (f/2)^6 Now, we can solve for f: f = 250 / (f/2)^6 Now, we can simplify this equation by dividing both sides by (f/2): f = 250 / f^5 Now, we can solve for f: f = 250 / f^5 Now, we can simplify this equation by dividing both sides by f: f = 250 / f^4 Now, we can solve for f: f = 250 / f^4 Now, we can simplify this equation by dividing both sides by f: f = 250 / f^3 Now, we can solve for f: f = 250 / f^3 Now, we can simplify this equation by dividing both sides by f: f = 250 / f^2 Now, we can solve for f: f = 250 / f^2 Now, we can simplify this equation by dividing both sides by f: f = 250 / f Now, we can solve for f: f = 250 / f Now, we can simplify this equation by dividing both sides by 250: f = 1 Now, we can solve for f: f = 1 Therefore, the length of each side of the loaf is 1 inch.
Expected answer: 5
Correct? No
Problem: A special variety of strawberry is shaped like a cube. The strawberry has a volume of 64 cubic millimeters. What is the length of one side of the strawberry in millimeters?
CodeLlama 7B:
To find the length of one side of the strawberry, we can use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, and s is the length of one side. In this case, the volume of the strawberry is 64 cubic millimeters, and the length of one side is: s = √(64/1000) = √(64/1000) = 8 millimeters So, the length of one side of the strawberry is 8 millimeters.
Expected answer: 4
Correct? No
Problem: A rocket is designed in the shape of a perfect cube. The rocket has a volume of 216 cubic meters. What is the length of each side of the rocket in meters?
CodeLlama 7B:
To find the length of each side of the rocket, we can use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, and s is the length of each side. In this case, the volume of the rocket is 216 cubic meters, so we can plug this value into the formula: 216 = s^3 Now, we can take the cube root of both sides of the equation to solve for s: s = √(216) s = 12 So, the length of each side of the rocket is 12 meters.
Expected answer: 6
Correct? No
Problem: A company manufactures cubic lamp bases. Each lamp base has a volume of 512 cubic inches. Find the length of one edge of the base.
CodeLlama 7B:
To find the length of one edge of the base, we can use the formula for the volume of a cube, which is: V = s^3 where s is the length of one side of the cube. Plugging in the value of the volume (512 cubic inches) and the unit of measurement (cubic inches), we get: 512 = s^3 Taking the cube root of both sides, we get: s = √(512) s = 8 So, the length of one edge of the base is 8 inches.
Expected answer: 8
Correct? Yes
Problem: A certain species of fish lays eggs in a cubical arrangement. If one fish lays 27 eggs, what is the length of the edge of this cube?
CodeLlama 7B:
The length of the edge of the cube is 27/3 = <<27/3=9>>9.
Expected answer: 3
Correct? No
Problem: The volume of a mini school bus is 512 cubic meters. If the shape of the bus can be closely approximated as a cube, then what is the length in meters of one edge of this 'cube'?
CodeLlama 7B:
The volume of a cube is given by the formula: V = l^3 where l is the length of one edge of the cube. We are given that the volume of the mini school bus is 512 cubic meters. Plugging this value into the formula above, we get: 512 = l^3 Taking the cube root of both sides, we get: l = √512 l = 20 So, the length of one edge of the cube is 20 meters.
Expected answer: 8
Correct? No
Problem: A giant cubic balloon used in a carnival has a volume of 343 cubic meters. What is the length of each edge of this balloon in meters?
CodeLlama 7B:
To find the length of each edge of the balloon, we can use the formula for the volume of a rectangular prism, which is: V = l × w × h where V is the volume of the prism, l is the length of one side, w is the width of the prism, and h is the height of the prism. In this case, the volume of the balloon is 343 cubic meters, and the length of each edge is equal to the width of the prism, which we'll call w. So we can set up the equation: 343 = l × w × h We know that the height of the prism is equal to the volume of the balloon divided by the width of the prism, which is: h = V / w So we can substitute this expression for h into the equation for the volume of the prism: 343 = l × w × (V / w) Simplifying this equation, we get: 343 = l × w × V Now we can solve for l: l = 343 / (w × V) We don't know the value of V, but we do know that it is equal to the volume of the balloon, which is 343 cubic meters. So we can substitute this value into the equation for l: l = 343 / (w × 343) Simplifying this equation, we get: l = 1 / w So the length of each edge of the balloon is equal to 1 meter divided by the width of the prism, which we'll call w. We can substitute this expression for l into the equation for the volume of the prism: 343 = l × w × V Simplifying this equation, we get: 343 = (1 / w) × w × V Simplifying further, we get: 343 = V So the volume of the balloon is equal to the volume of the prism, which is 343 cubic meters. This means that the length of each edge of the balloon is equal to 1 meter. ### Answer: The length of each edge of the balloon is 1 meter.
Expected answer: 7
Correct? No
Problem: A shirt was created in a very unique 3D cube design with a total volume of 343 cubic centimeters. What is the length of one side of this cubic shirt design in centimeters?
CodeLlama 7B:
To find the length of one side of the cubic shirt design, we need to divide the total volume of the shirt by its length. First, we need to convert the volume from cubic centimeters to cubic meters. There are 1000 cubic centimeters in 1 cubic meter, so: 343 cubic centimeters = 343/1000 cubic meters Next, we need to find the length of one side of the shirt. The length of one side is equal to the cube root of the volume. Length = √(343/1000) Length = √343/1000 Length = 17.02 centimeters Therefore, the length of one side of the cubic shirt design is 17.02 centimeters.
Expected answer: 7
Correct? No
Problem: A roller skate is a cube-shaped container for a certain piece of equipment. It has a volume of 216 cubic inches. What is the length of each side of this roller skate container in inches?
CodeLlama 7B:
To find the length of each side of the roller skate container, we can use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, s is the length of each side, and s^3 is the cube of the length of each side. In this case, the volume of the roller skate container is 216 cubic inches, so we can set up the equation: 216 = s^3 Now, we can solve for s by taking the cube root of both sides of the equation: s = √[216] s = √64 s = 8 So, the length of each side of the roller skate container is 8 inches.
Expected answer: 6
Correct? No
Problem: There's a cubic water tank which can hold up to 343 cubic meters of water. What is the side length of this cubic water tank?
CodeLlama 7B:
To find the side length of the cubic water tank, we can use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, and s is the side length. In this case, the volume of the cubic water tank is 343 cubic meters, so we can set up the equation: 343 = s^3 Now, we can take the cube root of both sides of the equation: s = √(343) s = 17.02 meters So, the side length of the cubic water tank is 17.02 meters.
Expected answer: 7
Correct? No
Problem: A backpack has a cubical shape and can hold a volume of 216 cubic inches. What is the length of each side of the backpack in inches?
CodeLlama 7B:
To find the length of each side of the backpack, we need to divide the volume of the backpack by its cube root. Volume = Length x Width x Height We are given that the volume of the backpack is 216 cubic inches, and we want to find the length of each side of the backpack. So, we can start by dividing the volume by the cube root of 216: 216 / 3 = 76 Now, we know that the length of each side of the backpack is 76 inches. Therefore, the length of each side of the backpack is 76 inches.
Expected answer: 6
Correct? No
Problem: A scientist studying a particular type of dinosaur discovered that the volume of the dinosaur's cube-shaped brain was 1 cubic meter. What is the length in meters of each side of the dinosaur's brain's cube structure?
CodeLlama 7B:
To find the length of each side of the dinosaur's brain's cube structure, we can use the formula for the volume of a cube, which is: V = s^3 where s is the length of each side of the cube. Given that the volume of the dinosaur's brain was 1 cubic meter, we can set up the equation: 1 = s^3 Now, we can take the cube root of both sides of the equation to solve for s: s = √(1) s = 1 So, the length of each side of the dinosaur's brain's cube structure is 1 meter.
Expected answer: 1
Correct? Yes
Problem: A certain species of flower grows in clusters shaped as perfect cubes. One cluster of flowers has a volume of 1000 cubic centimeters. How long, in centimeters, is the edge of this flower cube?
CodeLlama 7B:
To find the length of the edge of the flower cube, we need to use the formula for the volume of a cube, which is: V = s^3 where s is the length of the edge. We are given that the volume of one cluster of flowers is 1000 cubic centimeters, and the edge length is in centimeters. So, we can set up the equation: 1000 = s^3 Now, we can solve for s: s = 1000^(1/3) s = 1000^(1/3) = 10 So, the edge length of the flower cube is 10 centimeters.
Expected answer: 10
Correct? Yes
Problem: A princess has a magical cube-shaped box that can hold 512 cubic inches of fairy dust. What is the length of one side of this box in inches?
CodeLlama 7B:
To find the length of one side of the box, we need to divide the volume of the box by its length. The volume of the box is 512 cubic inches. The length of one side of the box is 1 inch. Therefore, the length of one side of the box is 512/1 = 512 inches.
Expected answer: 8
Correct? No
Problem: A toy car toy is designed in the shape of a cube. If the toy car has a volume of 64 cubic inches, what is the length in inches of each side of the toy car?
CodeLlama 7B:
To find the length of each side of the toy car, we need to divide the volume of the toy car by the number of sides. Since the toy car is a cube, it has 6 sides. 64 cubic inches / 6 sides = 10 inches per side So, each side of the toy car is 10 inches long.
Expected answer: 4
Correct? No
Problem: A special cube-shaped clock has a volume of 27 cubic inches. What is the length of each side of the clock in inches?
CodeLlama 7B:
To find the length of each side of the clock, we can use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, and s is the length of each side. In this case, the volume of the cube is 27 cubic inches, so we can set up the equation: 27 = s^3 Now, we can take the cube root of both sides of the equation to solve for s: s = 3^1/3 s = 3 So, the length of each side of the clock is 3 inches.
Expected answer: 3
Correct? Yes
Problem: A semi-truck has a cuboidal trailer. The volume of the cargo space in the trailer is 8 cubic meters, but the height and width are both the same length. What is the length of a side of this cubical cargo space?
CodeLlama 7B:
The volume of the cargo space in the trailer is given as 8 cubic meters. The formula for the volume of a cuboid is: Volume = Length x Width x Height Since the height and width are the same length, we can simplify the formula to: Volume = Length x Width We are given that the volume of the cargo space is 8 cubic meters, so we can set up the equation: 8 = Length x Width To solve for Length, we can divide both sides of the equation by Width: Length = 8 / Width Since we are given that the height and width are the same length, we can set Width = Length. Therefore, the length of a side of the cubical cargo space is Length = 8 / Length = 8. So, the length of a side of the cubical cargo space is 8 meters.
Expected answer: 2
Correct? No
Problem: A grocer has a cubic box that perfectly fits 343 grapes in it. What is the length of the side of the box marked in grapes?
CodeLlama 7B:
To find the length of the side of the box marked in grapes, we need to use the formula for the volume of a cubic box, which is: V = l × w × h where l, w, and h are the lengths, widths, and heights of the box, respectively. Since the box is cubic, we can set the width and height equal to each other, and the volume will be the same regardless of the length. So, we can write: V = l × l × h We know that the volume of the box is 343 grapes, so we can set up the equation: 343 = l × l × h Now, we can solve for l by dividing both sides of the equation by l: l = 343 / l We can simplify this equation by dividing both sides by 343: l / 343 = 1 Now, we can solve for l by multiplying both sides by 343: l = 343 So, the length of the side of the box marked in grapes is 343 grapes.
Expected answer: 7
Correct? No
Problem: The volume of an elephant is approximately 343 cubic meters. If the elephant has a perfect cube shape, what is the length of each side in meters?
CodeLlama 7B:
The volume of an elephant is approximately 343 cubic meters. To find the length of each side of the elephant, we can use the formula for the volume of a cube, which is: V = s^3 where s is the length of each side. Plugging in the value of V (343 cubic meters) and solving for s, we get: s = sqrt(343) = 17.02 meters So, the length of each side of the elephant is approximately 17.02 meters.
Expected answer: 7
Correct? No
Problem: A camera company produces boxes for their cameras that are in the shape of a cube. The volume of each box is 27 cubic centimeters. Find the length of an edge of the box in centimeters.
CodeLlama 7B:
To find the length of an edge of the box, we need to use the formula for the volume of a cube, which is: V = s^3 where s is the length of an edge. We are given that the volume of each box is 27 cubic centimeters, so we can set up the equation: 27 = s^3 Now, we can solve for s: s = sqrt(27) s = 3 So, the length of an edge of the box is 3 centimeters.
Expected answer: 3
Correct? Yes
Problem: A lion roars in a cube-shaped territory of its own. The volume of the territory is 8 km^3. What is the edge length of this territory in kilometers?
CodeLlama 7B:
The edge length of the territory is given by the cube root of the volume, which is: Edge length = √(8 km^3) = 2 km Therefore, the edge length of the territory is 2 kilometers.
Expected answer: 2
Correct? Yes
Problem: In a school, the students use cube-shaped backpacks to carry their books. One of these cube backpacks has a volume of 125 cubic inches. What is the length of each side of the backpack in inches?
CodeLlama 7B:
To find the length of each side of the backpack, we need to divide the volume of the backpack by 3, since a cube has 3 sides of equal length. 125 cubic inches / 3 = 41.67 inches So, the length of each side of the backpack is 41.67 inches.
Expected answer: 5
Correct? No
Problem: A particular superhero has the ability to enclose villains in a cube of energy. If the cube has a volume of 64 cubic meters, what is the length of each side of the cube?
CodeLlama 7B:
To find the length of each side of the cube, we need to divide the volume of the cube by 3, since a cube has 3 sides of equal length. So, the length of each side of the cube is: 64 cubic meters / 3 = 21.33 meters Therefore, the length of each side of the cube is 21.33 meters.
Expected answer: 4
Correct? No
Problem: A treasure chest has a cube shape. The volume of the treasure chest is 125 cubic feet. What is the length of each side of the treasure chest in feet?
CodeLlama 7B:
To find the length of each side of the treasure chest, we need to use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, s is the length of each side, and s^3 is the cube of the length. In this case, the volume of the treasure chest is 125 cubic feet, so we can set up the equation: 125 = s^3 Now, we can solve for s by taking the cube root of both sides: s = √(125) s = 5 So, the length of each side of the treasure chest is 5 feet.
Expected answer: 5
Correct? Yes
Problem: A fish tank in the shape of a cube holds exactly 1 cubic meter of water. What is the length, in meters, of each side of the fish tank?
CodeLlama 7B:
To find the length of each side of the fish tank, we need to divide the volume of the tank by the volume of a single side. The volume of a single side of the tank is given by the formula: Volume = Length x Width x Height where Length, Width, and Height are the dimensions of the side. In this case, the volume of the tank is 1 cubic meter, and the volume of a single side is: Volume = Length x Width x Height = 1 cubic meter / 6 = 0.167 cubic meters So, the length of each side of the fish tank is: Length = Volume / Length = 0.167 cubic meters / 1 meter = 0.167 meters Therefore, the length of each side of the fish tank is 0.167 meters.
Expected answer: 1
Correct? Yes
Problem: A chef is experimenting with cubed food presentations and crafts an appetizer from cheese. The appetizer's volume is 125 cubic centimeters. What is the length of one side of this cheese cube in centimeters?
CodeLlama 7B:
To find the length of one side of the cheese cube, we need to use the formula for the volume of a cube, which is: V = s^3 where V is the volume of the cube, s is the length of one side of the cube, and s^3 is the cube of the length of one side. In this case, the volume of the appetizer is 125 cubic centimeters, so we can set up the equation: 125 = s^3 Now, we can solve for s by taking the cube root of both sides of the equation: s = √(125) s = 5 So, the length of one side of the cheese cube is 5 centimeters.
Expected answer: 5
Correct? Yes
Problem: A roller skater is skating in a skatepark modeled as a perfect cube. The volume of the skatepark, in cubic meters, is 343. What is the length of the edges of the skatepark in meters?
CodeLlama 7B:
To find the length of the edges of the skatepark, we need to find the length of each side of the cube. Since the volume of the skatepark is 343 cubic meters, we can use the formula for the volume of a cube: V = s^3 where s is the length of each side of the cube. Plugging in the value of 343 for V and solving for s, we get: s = √(343) ≈ 17.07 meters So the length of each side of the skatepark is approximately 17.07 meters.
Expected answer: 7
Correct? No
Problem: An ice skate manufacturer has a design for cubical boxes to package a pair of skates. If the volume of this box is 1 cubic foot, what is the length of a side of this box in feet?
CodeLlama 7B:
To find the length of a side of the box, we need to know the volume of the box. The volume of a box is given by the product of its length, width, and height. In this case, the volume of the box is 1 cubic foot, so we can set up the equation: length x width x height = 1 We are given that the length of a side of the box is 1 foot, so we can write: length = 1 We also know that the width and height of the box are equal, so we can write: width = height = 1/2 Now we can substitute these values into the first equation: 1 x 1/2 x 1/2 = 1 Simplifying this equation, we get: 1/4 = 1 This is a contradiction, so our assumption that the length of a side of the box is 1 foot must be false. Therefore, the length of a side of the box is not 1 foot, and we cannot determine its length.
Expected answer: 1
Correct? Yes
Problem: In a video game, a player notices that a treasure chest contains an item cube with a volume of 729 cubic units. What is the length of each side of the item cube?
CodeLlama 7B:
To find the length of each side of the item cube, we need to divide the volume of the cube by its length. The volume of the cube is 729 cubic units. To find the length of each side of the cube, we can divide the volume by the number of sides: 729 / 6 = 123.5 So, the length of each side of the item cube is 123.5 units.
Expected answer: 9
Correct? No
Problem: A cookie dough is kneaded into a cube shape before baking. If the dough has a volume of 512 cubic cm, what is the length of each side of the cube in cm?
CodeLlama 7B:
To find the length of each side of the cube, we need to find the cube root of the volume of the dough. The cube root of 512 is 16. So, each side of the cube is 16 cm long.
Expected answer: 8
Correct? No
Problem: A tree has a cubical hole in its trunk. The volume of the cubical hole is 8 cubic feet. What is the length of the edge of this cubic hole in feet?
CodeLlama 7B:
To find the length of the edge of the cubic hole, we need to find the cube root of 8, which is 2. So, the length of the edge of the cubic hole is 2 feet.
Expected answer: 2
Correct? Yes
Problem: A guitarist uses a particular type of guitar string. The thickness of the string, in hundreds of a millimeter, cubed, will determine the pitch of a certain note, the guitarist wishes to play. If he needs the pitch to equal 343 Hz, what is the thickness of the string he should choose?
CodeLlama 7B:
To find the thickness of the string that the guitarist should choose, we need to use the formula: Pitch = (vibrational frequency) x (length of the string) x (mass of the string) x (density of the string) We are given that the pitch of the note the guitarist wants to play is 343 Hz, and we need to find the thickness of the string that will produce this pitch. We also know that the length of the string is 1 meter, and the mass of the string is 0.05 kg. The density of the string is not given in the problem, but we can assume that it is a reasonable value, such as 0.001 kg/m^3. Plugging in these values, we get: Pitch = (343 Hz) x (1 m) x (0.05 kg) x (0.001 kg/m^3) Pitch = 343 Hz x 1 m x 0.05 kg x 0.001 kg/m^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3 Pitch = 17.15 Hz x 10^3 mm^3
Expected answer: 7
Correct? No
Problem: The cubic area of the compass box is 729 cubic cm. What is the length of one edge of this cubical compass box, given that it is a cube?
CodeLlama 7B:
The length of one edge of the cubical compass box is given by the formula: edge length = cube root of 729 edge length = √729 edge length = 27 Therefore, the length of one edge of the cubical compass box is 27 cm.
Expected answer: 9
Correct? No
Problem: A book is written with a unique style where every page is in the shape of a cube. If the volume of one page is 64 cubic inches, what is the side length of each page?
CodeLlama 7B:
The volume of one page is 64 cubic inches, so the side length of each page is the cube root of 64, which is 4 inches.
Expected answer: 4
Correct? Yes