Mixtral 8x22B 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. To find the length of one side, we can take the cube root of the volume. The cube root of 512 is <<cbrt(512)=8>>8 feet. ### Answer: 8 feet
Expected answer: 8
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Therefore, to find the length of each side of the fireplace, we need to find the cube root of the volume. The cube root of 729 is 9. Therefore, the length of each side of the fireplace is 9 feet. ### Answer: 9 feet
Expected answer: 9
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. To find the length of one side, we can take the cube root of the volume. s = ∛1000 = <<∛1000=10>>10 meters. ### Answer: 10 meters
Expected answer: 10
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by multiplying the length of one side by itself three times. Let x be the length of one side of the tank. x^3 = 512 x = ∛512 = <<∛512=8>>8 ### Answer: 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?
Mixtral 8x22B:
Reasoning: Since the mountain has a cuboidal shape and all of its sides are of equal length, it is a cube. The volume of a cube is given by the formula V = s^3, where s is the length of one side. Let s be the length of one side of the cube. Then, we have: V = s^3 64 = s^3 To find the length of one side, we take the cube root of both sides: s = ∛64 s = 4 Therefore, the length of each side of the cuboid is 4 kilometers. ### Answer: 4 kilometers
Expected answer: 4
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. To find the length of an edge, we can take the cube root of the volume. The cube root of 512 is 8, so the length of each edge of the crater is 8 kilometers. ### Answer: 8 kilometers
Expected answer: 8
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The number of blocks in a cube is equal to the cube of the length of one side. Let x be the length of one side of the cube. x^3 = 343 x = ∛343 x = <<∛343=7>>7 ### Answer: 7
Expected answer: 7
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. So, if the volume of the substance is 512 cubic feet, then the length of one side of the cubic container is the cube root of 512. The cube root of 512 is 8, so the length of one side of the cubic container is 8 feet. ### Answer: 8 feet
Expected answer: 8
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is found by cubing the length of one of its edges. Let x be the length of one edge of the cube. Then, x^3 = 512 mm^3. To find the length of one edge, we take the cube root of 512. x = ∛512 = <<∛512=8>>8 mm. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. If the volume of the cube is 8 cubic cm, then s^3 = 8. Taking the cube root of both sides, we get s = 8^(1/3) = <<8^(1/3)=2>>2 cm. ### Answer: 2 cm
Expected answer: 2
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by the formula V = a^3, where a is the length of one edge. To find the length of one edge, we can take the cube root of the volume. The cube root of 27 is 3. ### Answer: 3 kilometers
Expected answer: 3
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Since the volume of the box is 1 cubic inch, we have 1 = s^3. Taking the cube root of both sides, we get s = 1^(1/3) = <<1^(1/3)=1>>1 inch. ### Answer: 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?
Mixtral 8x22B:
Reasoning: Since each cubic centimeter holds 1 milliliter of nectar, the volume of the flower in cubic centimeters is equal to the amount of nectar it holds in milliliters. Therefore, the volume of the flower is 125 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. To find the length of one side of the cubic flower, we can take the cube root of the volume: s = ∛(125) = <<∛(125)=5>>5 centimeters. ### Answer: 5 centimeters
Expected answer: 5
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. To find the length of one side, we can take the cube root of the volume. The cube root of 125 is 5. Therefore, the length of one side of the tree stump is 5 meters. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. To find the length of an edge, we can take the cube root of the volume. The cube root of 1000 is <<1000^(1/3)=10>>10 millimeters. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. Since the volume of the soap is 1 cubic cm, we have 1 = s^3. Taking the cube root of both sides, we get s = 1 cm. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. To find the length of an edge, we can take the cube root of the volume. The cube root of 216 is 6. Therefore, the length of each edge of the yew tree is 6 meters. ### Answer: 6 meters
Expected answer: 6
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side of the cube. To find the length of one side of the cube, we can take the cube root of the volume. The cube root of 1000 is <<1000^(1/3)=10>>10 cm. ### Answer: 10 cm <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <</SYS>> <
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Let x be the length of one side of the cube. Then, x^3 = 125. To find the length of one side, we take the cube root of 125. x = ∛125 = <<∛125=5>>5 centimeters. ### Answer: 5 centimeters
Expected answer: 5
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. To find the length of a side, we can take the cube root of the volume. The cube root of 125 is 5. Therefore, the length of each side of the bottle is 5 centimeters. ### Answer: 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?
Mixtral 8x22B:
Reasoning: Since the building has a cuboidal structure with a uniform cross-sectional area and all sides are equal, it is a cube. Let the length of one side be x meters. The volume of a cube is given by V = x^3. Given that the volume of the building is 216 cubic meters, we have x^3 = 216. Taking the cube root of both sides, we get x = 6. ### Answer: 6 meters
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Let x be the length of one side of the cube. Then, x^3 = 343. Taking the cube root of both sides, we get x = 7. Therefore, the length of each side of the chair is 7 feet. ### Answer: 7 feet
Expected answer: 7
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by the formula V = s^3, where s is the length of a side. To find the length of a side, we can take the cube root of the volume. The cube root of 729 is 9. ### Answer: 9 inches
Expected answer: 9
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. To find the length of an edge, we can take the cube root of the volume. The cube root of 8 is 2. Therefore, the length of each edge of the spaceship is 2 miles. ### Answer: 2 miles
Expected answer: 2
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is equal to the length of one side raised to the third power. Let x be the length of one side of the cube. x^3 = 343 x = ∛343 = <<∛343=7>>7 ### Answer: 7 feet
Expected answer: 7
Correct? Yes
Problem: The volume of the compass cube is 8 cubic inches. What is the length of the edge of the compass cube in inches?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of the edge of the cube. So, s^3 = 8 cubic inches. Taking the cube root of both sides, we get s = 8^(1/3) = <<8^(1/3)=2>>2 inches. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by multiplying the length of one side by itself three times (side^3). To find the length of one side of the cube, we need to find the cube root of the volume. The cube root of 729 is 9. ### Answer: 9 meters
Expected answer: 9
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: Since the slide has a cuboid shape and the same length, width, and height, it is a cube. The volume of a cube is given by the formula V = s^3, where s is the length of one side. To find the length of one side, we can take the cube root of the volume: s = ∛V = ∛1000 = <<∛1000=10>>10 feet. ### Answer: 10 feet
Expected answer: 10
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. So, if the volume of the cube is 512 cubic feet, then the length of each side is the cube root of 512. The cube root of 512 is 8, so the length of each side of the play cube is 8 feet. ### Answer: 8 feet
Expected answer: 8
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one edge. We know that V = 27 cubic centimeters, so we can set up the equation 27 = s^3. Taking the cube root of both sides, we get s = 3 centimeters. ### Answer: 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?
Mixtral 8x22B:
Reasoning: Since the container is cube-shaped, each side of the cube holds the cube root of the total number of grapes. The cube root of 27 is 3. ### Answer: 3 grapes per side
Expected answer: 3
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side of the cube. To find the length of one side of the cube container, we can take the cube root of the volume. s = ∛216 = <<∛216=6>>6 meters. ### Answer: 6 meters
Expected answer: 6
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. To find the length of an edge, we can take the cube root of the volume. The cube root of 64 is 4, so the length of each edge of the cube charm is 4 mm. ### Answer: 4 mm
Expected answer: 4
Correct? Yes
Problem: If a number is cubed and the result is 64, what is the number?
Mixtral 8x22B:
Reasoning: The cube root of 64 is 4. ### Answer: 4
Expected answer: 4
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: 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 know that the volume of the mug is 1 liter, so we can set up the equation 1 = s^3 and solve for s. Taking the cube root of both sides, we get s = 1^(1/3) = <<1^(1/3)=1>>1 liter. So each side of the petite mug is 1 liter long. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is equal to the length of one side cubed. Let x be the length of one side of the cube-shaped blanket. x^3 = 343 x = ∛343 = <<∛343=7>>7 inches ### Answer: 7 inches
Expected answer: 7
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is found by cubing the length of one of its sides. Since the volume of the larger cube is 729 cubic cm, we can find the length of one side of the larger cube by taking the cube root of 729. The cube root of 729 is 9 cm. Since the larger cube is made up of smaller cubes, the length of one side of the smaller cube must be a factor of 9 cm. The only factor of 9 that is a whole number is 3 cm. Therefore, the length of one side of the smaller ice cube is 3 cm. ### Answer: 3 cm
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Let x be the length of one side of the cube. Then, x^3 = 216 To find the length of one side, we take the cube root of 216. x = ∛216 = <<∛216=6>>6 cm ### Answer: 6 cm
Expected answer: 6
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. To find the length of an edge, we can take the cube root of the volume. The cube root of 216 is <<216^(1/3)=6>>6 millimeters. ### Answer: 6 millimeters
Expected answer: 6
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side of the cube. To find the length of one side of the snail's cubical shell, we can take the cube root of the volume: s = ∛V = ∛27 = <<∛27=3>>3 cm. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. To find the length of one side, we can take the cube root of the volume. The cube root of 27 is 3. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one edge. To find the length of one edge, we need to take the cube root of the volume. The cube root of 216 is 6. ### Answer: 6 feet
Expected answer: 6
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one side. Let x be the length of one side of the cube. Then, x^3 = 216 To find the length of one side, we take the cube root of 216. x = ∛216 = <<∛216=6>>6 inches ### Answer: 6 inches
Expected answer: 6
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its edges. Let x be the length of one edge of the cube. Then, x^3 = 125 cubic inches. To find the length of one edge, we need to take the cube root of 125. x = ∛125 = <<∛125=5>>5 inches. ### Answer: 5 inches
Expected answer: 5
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The number of flowers used is equal to the volume of the cube. The volume of a cube is given by the formula V = s^3, where s is the length of a side. So, 125 = s^3. To find the length of a side, we take the cube root of 125. The cube root of 125 is 5. Therefore, the length of each side of the flower cube is 5. ### Answer: 5
Expected answer: 5
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. To find the length of a side, we can take the cube root of the volume. The cube root of 1000 is <<1000^(1/3)=10>>10 centimeters. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. To find the length of one side, we can take the cube root of the volume. The cube root of 27 is 3, so the length of one side of the cargo hold is 3 meters. ### Answer: 3 meters
Expected answer: 3
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side of the cube. To find the length of one side of the cube, we can take the cube root of the volume. The cube root of 216 is 6, so the length of each side of the cubic cucumber is 6 centimeters. ### Answer: 6 centimeters
Expected answer: 6
Correct? Yes
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)?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one edge. To find the length of one edge, we need to take the cube root of the volume. The cube root of 729 is 9. ### Answer: 9 feet
Expected answer: 9
Correct? Yes
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.)
Mixtral 8x22B:
Reasoning: The cube root of 27 is 3. The letter that corresponds to the position 3 in the alphabet is 'c'. ### Answer: 'c'
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. Since the volume of the buoy is 1 cubic foot, we have 1 = s^3. Taking the cube root of both sides, we get s = 1^(1/3) = <<1^(1/3)=1>>1 foot. ### Answer: 1 foot
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?
Mixtral 8x22B:
Reasoning: Let's denote the length of the object as L. The temperature at the heart of the object is proportional to the cube of its length, so we can write the following equation: Temperature = k \* L^3 where k is a constant of proportionality. We know that the temperature at the heart of the object is 729 degrees, so we can substitute this value into the equation: 729 = k \* L^3 To find the value of k, we can rearrange the equation: k = 729 / L^3 Since the object is cubical, all of its sides are equal in length. Therefore, the length of the object is equal to the cube root of its volume. The volume of a cube is given by the formula: Volume = L^3 Since the temperature is directly proportional to the cube of the length, we can substitute the volume for the length in the equation: 729 = k \* Volume Now we can solve for the volume: Volume = 729 / k Since the object is cubical, the length of the object is equal to the cube root of its volume: L = cube root(Volume) L = cube root(729 / k) Since the temperature is directly proportional to the cube of the length, we can substitute the temperature for the length in the equation: L = cube root(729) L = 9 Therefore, the length of the object is 9 units. ### Answer: 9
Expected answer: 9
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by the formula V = s^3, where s is the length of a side. So, s^3 = 8. Taking the cube root of both sides, we get s = ∛8 = <<∛8=2>>2 centimeters. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one edge. To find the length of one edge, we can take the cube root of the volume. The cube root of 729 is 9. ### Answer: 9 centimeters
Expected answer: 9
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. To find the length of one side, we can take the cube root of the volume. The cube root of 125 is 5. Therefore, the length of one side of the compartment is 5 inches. ### Answer: 5 inches
Expected answer: 5
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. To find the length of a side, we can take the cube root of the volume. The cube root of 343 is 7, so the length of each side of the box is 7 inches. ### Answer: 7 inches
Expected answer: 7
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. To find the length of an edge, we need to take the cube root of the volume. The cube root of 512 is 8, so each edge of the candy package is 8 centimeters long. ### Answer: 8 centimeters
Expected answer: 8
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. To find the length of a side, we can take the cube root of the volume. The cube root of 512 is <<cbrt(512)=8>>8. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its edges. Let x be the length of one edge of the toothbrush. Then, x^3 = 729. Taking the cube root of both sides, we get x = 9. Therefore, the length of each edge of the toothbrush is 9 centimeters. ### Answer: 9 centimeters
Expected answer: 9
Correct? Yes
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)?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. To find the length of an edge, we can take the cube root of the volume. The cube root of 8 is 2. Therefore, the length of each edge of the star is 2 light years. ### Answer: 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?
Mixtral 8x22B:
Reasoning: Since the volume of a cube is given by the formula V = s^3, where s is the length of a side, and the volume of the chamber is 1 unit^3, we can set up the equation 1 = s^3. Solving for s, we find that s = 1^(1/3) = <<1^(1/3)=1>>1. Therefore, the length of each side of the cubical chamber is 1 unit. ### Answer: 1 unit
Expected answer: 1
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. To find the length of one side, we can take the cube root of the volume. The cube root of 1000 mm^3 is <<1000^(1/3)=10>>10 mm. ### Answer: 10 mm
Expected answer: 10
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one edge of the cube. To find the length of one edge of the cube, we can take the cube root of the volume. The cube root of 1 is 1, so the length of one edge of the cube is 1 meter. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. So, if the volume of the box is 216 cubic meters, then the length of each side is the cube root of 216. The cube root of 216 is 6. ### Answer: 6 meters
Expected answer: 6
Correct? Yes
Problem: A cube-shaped house has a volume of 64 cubic feet. What is the length of one side of the house in feet?
Mixtral 8x22B:
Reasoning: The volume of a cube is equal to the length of one side cubed. Let x be the length of one side of the house. x^3 = 64 x = 64^(1/3) = <<64^(1/3)=4>>4 feet ### Answer: 4 feet
Expected answer: 4
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. To find the length of an edge, we can take the cube root of the volume. The cube root of 1000 is <<1000^(1/3)=10>>10 centimeters. ### Answer: 10 centimeters
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side of the cube. The volume of the oven is 125 cubic inches, so we can set up the equation 125 = s^3 and solve for s. Taking the cube root of both sides, we get s = ∛125 = <<∛125=5>>5 inches. ### Answer: 5 inches
Expected answer: 5
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. To find the length of one side, we can take the cube root of the volume: s = ∛V = ∛64 = <<∛64=4>>4 millimeters. ### Answer: 4 millimeters
Expected answer: 4
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. To find the length of a side, we can take the cube root of the volume. The cube root of 216 is <<216^(1/3)=6>>6 meters. ### Answer: 6 meters
Expected answer: 6
Correct? Yes
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.
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one edge. To find the length of one edge, we can take the cube root of the volume. The cube root of 512 is 8. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The number of eggs laid by the fish is equal to the volume of the cube. The volume of a cube is given by the formula V = s^3, where s is the length of the edge of the cube. So, 27 = s^3. To find the length of the edge, we take the cube root of 27. s = ∛27 = <<∛27=3>>3 Therefore, the length of the edge of the cube is 3 units. ### Answer: 3 units
Expected answer: 3
Correct? Yes
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'?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one edge. To find the length of one edge, we can take the cube root of the volume. s = ∛512 = <<∛512=8>>8 meters. ### Answer: 8 meters
Expected answer: 8
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. To find the length of an edge, we can take the cube root of the volume. The cube root of 343 is 7. ### Answer: 7 meters
Expected answer: 7
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by the formula V = s^3, where s is the length of one side of the cube. To find the length of one side of the cube, we need to find the cube root of the volume. The cube root of 343 is <<343^(1/3)=7>>7. ### Answer: 7 centimeters
Expected answer: 7
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. To find the length of one side, we can take the cube root of the volume. The cube root of 216 is 6. Therefore, the length of each side of the roller skate container is 6 inches. ### Answer: 6 inches
Expected answer: 6
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the side length of the cube. To find the side length of the cubic water tank, we need to take the cube root of the volume. The cube root of 343 is 7, so the side length of the cubic water tank is 7 meters. ### Answer: 7 meters
Expected answer: 7
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Let x be the length of one side of the backpack. Then, x^3 = 216. To find the length of one side, we take the cube root of 216. x = ∛216 = <<∛216=6>>6 inches. ### Answer: 6 inches
Expected answer: 6
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side of the cube. Since the volume of the dinosaur's brain is 1 cubic meter, we can set up the equation 1 = s^3 and solve for s. Taking the cube root of both sides, we get s = 1^(1/3) = <<1^(1/3)=1>>1 meter. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. To find the length of an edge, we can take the cube root of the volume. The cube root of 1000 is <<1000^(1/3)=10>>10 centimeters. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is equal to the length of one side cubed. Let x be the length of one side of the box. x^3 = 512 x = 512^(1/3) x = <<512^(1/3)=8>>8 inches ### Answer: 8 inches
Expected answer: 8
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Let x be the length of one side of the cube. Then, x^3 = 64. Taking the cube root of both sides, we get x = 4. Therefore, the length of each side of the toy car is 4 inches. ### Answer: 4 inches
Expected answer: 4
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. To find the length of a side, we can take the cube root of the volume. The cube root of 27 is 3, so the length of each side of the clock is 3 inches. ### Answer: 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?
Mixtral 8x22B:
Reasoning: Since the volume of a cube is given by the formula V = s^3, where s is the length of a side, we can find the length of a side by taking the cube root of the volume. The volume of the cubical cargo space is 8 cubic meters, so the length of a side is s = ∛8 = <<∛8=2>>2 meters. ### Answer: 2 meters
Expected answer: 2
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The number of grapes that can fit in the box is a perfect cube, which means that the length of the side of the box is the cube root of the number of grapes. The cube root of 343 is 7, so the length of the side of the box is 7 grapes. ### Answer: 7 grapes
Expected answer: 7
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Let x be the length of one side of the cube. x^3 = 343 x = ∛343 = <<∛343=7>>7 ### Answer: 7 meters
Expected answer: 7
Correct? Yes
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.
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge of the cube. We are given that the volume of the box is 27 cubic centimeters, so we can set up the equation 27 = s^3. Taking the cube root of both sides, we get s = ∛27 = <<∛27=3>>3 centimeters. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the edge length. To find the edge length, we can take the cube root of the volume. s = ∛(8 km^3) = <<∛(8)=2>>2 km ### Answer: 2 km
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Let x be the length of one side of the backpack. Then, x^3 = 125 cubic inches. To find the length of one side, we take the cube root of 125. x = ∛125 = <<∛125=5>>5 inches. ### Answer: 5 inches
Expected answer: 5
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. To find the length of a side, we can take the cube root of the volume. The cube root of 64 is 4. Therefore, the length of each side of the cube is 4 meters. ### Answer: 4 meters
Expected answer: 4
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Let x be the length of one side of the treasure chest. x^3 = 125 x = ∛125 x = <<∛125=5>>5 ### Answer: 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?
Mixtral 8x22B:
Reasoning: Since the fish tank is a cube, all sides are equal in length. The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume is 1 cubic meter, we have 1 = s^3. Taking the cube root of both sides, we get s = 1 meter. ### Answer: 1 meter
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. So, if the volume of the cheese cube is 125 cubic centimeters, then the length of one side is the cube root of 125. The cube root of 125 is <<cbrt(125)=5>>5 centimeters. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of the edges of the cube. To find the length of the edges, we can take the cube root of the volume. The cube root of 343 is 7. Therefore, the length of the edges of the skatepark is 7 meters. ### Answer: 7 meters
Expected answer: 7
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Since the volume of the box is 1 cubic foot, we have 1 = s^3. Taking the cube root of both sides, we get s = 1^(1/3) = <<1^(1/3)=1>>1 foot. ### Answer: 1 foot
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Therefore, to find the length of each side of the item cube, we need to find the cube root of its volume. The cube root of 729 is <<cbrt(729)=9>>9. Therefore, the length of each side of the item cube is 9 units. ### Answer: 9 units
Expected answer: 9
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Let x be the length of one side of the cube. Then, x^3 = 512. Taking the cube root of both sides, we get x = 8. ### Answer: 8 cm
Expected answer: 8
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. We know that V = 8 cubic feet, so we can set up the equation 8 = s^3 and solve for s. Taking the cube root of both sides, we get s = ∛8 = <<∛8=2>>2 feet. ### Answer: 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?
Mixtral 8x22B:
Reasoning: The pitch of a string is determined by the formula: pitch = (1/2L) \* sqrt(T/m) where L is the length of the string, T is the tension, and m is the mass per unit length. Since the guitarist wants a pitch of 343 Hz, we can rearrange the formula to solve for m: m = T / (4 \* L^2 \* pitch^2) The thickness of the string is related to the mass per unit length by the formula: m = rho \* A where rho is the density of the string material and A is the cross-sectional area of the string. Since the thickness is given in hundreds of a millimeter, we can express the cross-sectional area as: A = (thickness/100)^2 \* pi Substituting this into the equation for m, we get: m = rho \* (thickness/100)^2 \* pi Now we can substitute this expression for m into the equation for pitch and solve for the thickness: 343 = (1/2L) \* sqrt(T / (rho \* (thickness/100)^2 \* pi)) Solving for thickness, we get: thickness = sqrt(T / (rho \* 4 \* L^2 \* 343^2 \* pi)) \* 100 Assuming the guitarist is using a standard guitar string with a length of 65 cm and a tension of 100 N, and the density of the string material is 7.85 g/cm^3, we can substitute these values into the equation and solve for the thickness: thickness = sqrt(100 / (7.85 \* 4 \* (0.65)^2 \* 343^2 \* pi)) \* 100 thickness = 0.028 cm Therefore, the guitarist should choose a string with a thickness of 0.028 cm. ### Answer: 0.028 cm
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of one edge. To find the length of one edge, we need to take the cube root of the volume. The cube root of 729 is 9. ### Answer: 9 cm
Expected answer: 9
Correct? Yes
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?
Mixtral 8x22B:
Reasoning: The volume of a cube is given by the formula V = s^3, where s is the side length of the cube. To find the side length of each page, we can take the cube root of the volume. The cube root of 64 is 4, so the side length of each page is 4 inches. ### Answer: 4 inches
Expected answer: 4
Correct? Yes