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 34B:

  To find the length of each side of the sandbox, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each side.

We are given that the sandbox has a volume of 512 cubic feet, so we can set up the equation:

512 = s^3

Now, we need to find the cube root of 512, which is 8. So, the length of each side of the sandbox is:

s = 8

Therefore, the length of each side of the sandbox is 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?

CodeLlama 34B:

  To find the length of each side of the fireplace, we need to find the cube root of the volume of the fireplace.

The volume of the fireplace is given as 729 cubic feet, so we can start by finding the cube root of 729:

729 = 3^3

So, the length of each side of the fireplace is:

3 feet

Therefore, the length of each side of the fireplace is 3 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 34B:

  To find the length of each side of the barn, we can use the formula for the volume of a rectangular prism, which is:

V = lwh

where l is the length, w is the width, and h is the height. Since the volume of the barn is given as 1000 cubic meters, we can set up the equation:

1000 = lwh

We know that the barn is cubical, so the length, width, and height are all equal. Let's call the length of one side "s". Then we can write:

1000 = s^3

Now we can solve for s:

s = 10^3

So the length of each side of the barn is 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?

CodeLlama 34B:

  To find the size of one side of the tank, 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 one side.

We are given that the volume of the tank is 512 m^3, so we can set up the equation:

512 = s^3

To solve for s, we can take the cube root of both sides:

s = 512^(1/3)

s ≈ 15.8 m

Therefore, the size of one side of the tank is approximately 15.8 meters.

Expected answer: 8

Correct? No

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 34B:

  Let's call the length of each side of the cuboid x.

Since the volume of the cuboid is given as 64 km^3, we can use the formula V = s \* l \* w, where s is the surface area of the cuboid and l and w are the lengths of the cuboid.

Since all sides of the cuboid are of equal length, we can say that the surface area of the cuboid is 6 \* x^2, since each side has area x^2.

So, we can set up the equation:

6 \* x^2 \* x = 64

Simplifying and solving for x, we get:

x = 4

So, the length of each side of the cuboid is 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?

CodeLlama 34B:

  To find the length of each edge of the crater, 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 edge.

We are given that the volume of the crater is 512 cubic kilometers, so we can set up the equation:

512 = s^3

To find the length of each edge, we can take the cube root of both sides of the equation:

s = 512^(1/3)

s = 8

So the length of each edge of the crater is 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?

CodeLlama 34B:

  To find the length of one side of the cube, we need to first find the total number of blocks on each side. Since the baby is building a cube structure, each side of the cube will have the same number of blocks.

Let's call the number of blocks on each side "x". Then, the total number of blocks on all sides of the cube will be 4x.

We know that the total number of blocks is 343, so we can set up the equation:

4x = 343

To solve for x, we can divide both sides by 4:

x = 343 / 4

x = 85.75

Since we can't have a fraction of a block, we round up to the nearest whole number:

x = 86

So, the length of one side of the cube is 86 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 34B:

  To find the length of one side of the cubic container, 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 one side of the cube.

We are given that the volume of the substance is 512 cubic feet, so we can set up the equation:

512 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 512^(1/3)

s = 8

So, the length of one side of the cubic container is 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?

CodeLlama 34B:

  To find the edge length of each eraser cube, we need to find the cube root of the volume of each cube.

The volume of each cube is given as 512 mm^3. To find the cube root of this number, we can use the formula:

cube root(x) = x^(1/3)

Plugging in the value of x = 512, we get:

cube root(512) = 512^(1/3)

Simplifying, we get:

cube root(512) = 8

So, 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 34B:

  To find the length of each side of the cube, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each side.

We are given that the volume of the cube is 8 cubic cm, so we can set up the equation:

8 = s^3

Now, we can solve for s:

s = 8^(1/3)

s = 2

So, the length of each side of the cube is 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?

CodeLlama 34B:

  Yes, I can calculate the length of one edge of the cube.

To do this, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the length of one edge of the cube.

We are given that the volume of the cube is 27 cubic kilometers, 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 = 27^(1/3)

s ≈ 3.002 kilometers

So, the length of one edge of the cube is approximately 3.002 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?

CodeLlama 34B:

  To find the length of each side of the box, we need to use the formula for the volume of a rectangular prism, which is:

V = l × w × h

where l is the length, w is the width, and h is the height. Since the volume of the box is 1 cubic inch, we can set up the equation:

1 = l × w × h

We know that the volume of the box is 1 cubic inch, so we can substitute this value into the equation:

1 = l × w × h

We also know that the length, width, and height of the box are equal, so we can substitute l = w = h:

1 = l × l × l

Simplifying the equation, we get:

1 = l^3

Taking the cube root of both sides, we get:

l = 1^1/3

l = 1

So, 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 34B:

  To find the length of one side of the cubic flower, we need to divide the volume of the flower by the volume of a single cubic centimeter.

The volume of the flower is 125 milliliters, which is equal to 125 cubic centimeters.

The volume of a single cubic centimeter is 1 milliliter, which is equal to 1 cubic centimeter.

So, to find the length of one side of the cubic flower, we can divide the volume of the flower by the volume of a single cubic centimeter:

125 cubic centimeters / 1 cubic centimeter = 125 centimeters

Therefore, 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 34B:

  To find the length of one side of the tree stump, 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 tree stump is 125 cubic meters, we can set up the equation:

125 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 125^1/3

s = 5

Therefore, 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 34B:

  To find the length of each edge of the bracelet, we need to use the formula for the volume of a rectangular prism, which is:

V = lwh

where l is the length, w is the width, and h is the height.

We know that the volume of the bracelet is 1000 cubic millimeters, so we can set up an equation using this information:

1000 = lwh

We also know that the bracelet is a cube, so the length, width, and height are all equal. Let's call the length of one edge "x" millimeters. Then we can write:

l = w = h = x

Substituting this into the equation above, we get:

1000 = x^3

To solve for x, we can take the cube root of both sides:

x = 10^3

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 34B:

  The volume of a cube is given by the formula V = s^3, where s is the length of each side. Since the volume of the soap is 1 cubic cm, we can set up the equation:

1 = s^3

To solve for s, we can take the cube root of both sides:

s = 1^1/3 = 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 34B:

  To find the length of each edge of the yew tree, we need to use the formula for the volume of a rectangular prism, which is:

Volume = Length x Width x Height

We know that the volume of the yew tree is 216 cubic meters, so we can set up an equation using this formula:

216 = L x W x H

We also know that the tree is a cubic yew tree, which means that all three dimensions (length, width, and height) are equal. So, we can let L = W = H.

Substituting this into the equation above, we get:

216 = L^3

Now, we can solve for L:

L = 216^(1/3)

L = 6

So, the length of each edge of the yew tree is 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?

CodeLlama 34B:

  To find the length of each side of the blanket, we can use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each side.

We are given that the volume of the blanket is 1000 cubic cm, so we can set up the equation:

1000 = s^3

To solve for s, we can take the cube root of both sides:

s = 10^1/3

So the length of each side of the blanket is 10^1/3 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 34B:

  To find the length of each side of the box, 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.

We are given that the volume of the box is 125 cubic centimeters, so we can set up the equation:

125 = s^3

To find the length of each side, we need to take the cube root of both sides of the equation:

s = 125^1/3

s = 5

So, the length of each side of the box is 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?

CodeLlama 34B:

  To find the length of each side of the bottle, 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 bottle is 125 cubic centimeters, so we can set up the equation:

125 = s^3

To find the length of each side, we can take the cube root of both sides of the equation:

s = 125^(1/3)

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 34B:

  Let's call the length of one side of the building "x" meters.

Since the building has a uniform cross-sectional area all along its height, we can assume that the cross-sectional area of the building is equal to the area of a square with side length "x".

The volume of the building is given as 216 cubic meters. We can calculate the volume of a rectangular prism with dimensions "x" meters by "x" meters by "x" meters as follows:

Volume = Length x Width x Height
= x x x x x
= x^3

Since the volume of the building is 216 cubic meters, we can set up the equation:

x^3 = 216

To solve for "x", we can take the cube root of both sides of the equation:

x = 3^3
= 27

Therefore, the length of one side of the building is 27 meters.

Expected answer: 6

Correct? No

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 34B:

  To find the length of each side of the chair, 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.

Given that the volume of the chair is 343 cubic feet, we can set up the equation:

343 = s^3

To find the length of each side, we can take the cube root of both sides of the equation:

s = 343^(1/3)

s = 3

So, the length of each side of the chair is 3 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 34B:

  To find the length of a side of each 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, and s is the length of a side of the cube.

We are given that the volume of each cube is 729 cubic inches, so we can set up the equation:

729 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 729^(1/3)

s = 3

So, the length of a side of each cube is 3 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 34B:

  To find the length of each edge of the spaceship, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each edge.

We are given that the volume of the spaceship is 8 cubic miles, so we can set up the equation:

8 = s^3

Now, we need to find the cube root of 8, which is 2.

So, the length of each edge of the spaceship is:

s = 2 miles

Therefore, the length in miles of each edge of the spaceship is 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?

CodeLlama 34B:

  To find the length of each side of the storage unit, 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 storage unit is 343 cubic feet, so we can set up the equation:

343 = s^3

To find the length of each side, we can take the cube root of both sides of the equation:

s = 343^(1/3)

s = 6

So, the length of each side of the storage unit is 6 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 34B:

  The volume of the compass cube is 8 cubic inches, which means that each edge of the cube has a length of 2 inches.

To see why, consider that the volume of a cube is given by the formula V = s^3, where s is the length of each edge. In this case, we know that V = 8, so we can solve for s:

s^3 = 8
s = 2

Therefore, the length of each 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 34B:

  To find the length of each side of the plot, we need to find the cube root of the volume of the plot.

The volume of the plot is given as 729 cubic meters, so we can start by finding the cube root of 729:

729^(1/3) = 3

So, the length of each side of the plot is 3 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 34B:

  To find the length of one side of the slide, we need to use the formula for the volume of a cuboid, which is:

V = lwh

where l is the length, w is the width, and h is the height. Since the volume is given as 1000 cubic feet, we can set up the equation:

1000 = lwh

Now, we need to find the length of one side of the slide. We can do this by dividing both sides of the equation by the area of the base of the slide, which is given by the product of the width and height:

1000 = lwh
1000 = l(wh)
1000 = l(lwh)/l
1000 = l^2

Now, we can take the square root of both sides of the equation to find the length of one side of the slide:

l = sqrt(1000)
l = 31.62 feet

Therefore, the length of one side of the slide is 31.62 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 34B:

  To find the length of each side of the play cube, we need to divide the volume of the cube (512 cubic feet) by the number of sides. Since the play cube has 6 sides, we can divide 512 by 6 to get the length of each side:

512 cubic feet ÷ 6 sides = 85.333333 feet

So, the length of each side of the play cube is approximately 85.333333 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 34B:

  Yes, I can help you with that!

To find the length of one edge of the hat, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the length of one edge of the cube.

We are given that the volume of the hat is 27 cubic centimeters, so we can set up the equation:

27 = s^3

Now, we need to find the cube root of both sides of the equation. The cube root of 27 is 3, so we can simplify the equation to:

s^3 = 3^3

s = 3

Therefore, 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 34B:

  To find out how many grapes each side of the cube holds, we need to divide the total number of grapes in the container by the number of sides of the cube.

Since each side of the cube has the same number of grapes, we can use the formula:

Number of grapes on each side = Total number of grapes / Number of sides

In this case, the total number of grapes in the container is 27, and the number of sides of the cube is 6.

So, we can plug these values into the formula:

Number of grapes on each side = 27 / 6

Number of grapes on each side = 4

Therefore, each side of the cube holds 4 grapes.

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 34B:

  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.

We are given that the volume of the container is 216 cubic meters, so we can set up the equation:

216 = s^3

Now, we need to find the value of s. To do this, we can take the cube root of both sides of the equation:

s = 216^(1/3)

s = 6

So, the length of one side of the cube container is 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?

CodeLlama 34B:

  To find the length of each edge of the cube charm, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each edge.

We are given that the volume of the cube charm is 64 mm^3, so we can set up the equation:

64 = s^3

To find the value of s, we can take the cube root of both sides of the equation:

s = 64^(1/3)

s = 4

So, the length of each edge of the cube charm is 4 mm.

Expected answer: 4

Correct? Yes

Problem: If a number is cubed and the result is 64, what is the number?

CodeLlama 34B:

  If a number is cubed and the result is 64, then the number is 4.

To see why, let's use the formula for cubing a number:

x^3 = 64

We can simplify this equation by taking the cube root of both sides:

x = 64^(1/3)

x = 4

Therefore, the number that, when cubed, gives 64 is 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?

CodeLlama 34B:

  Yes, I can help you with that!

Since the petite mug has a cubic shape and can hold 1 liter of hot drink, each side of the mug must be equal in length. Therefore, if the mug is 1 liter in capacity, each side of the mug will be 1 liter long.

So, 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 34B:

  To find the length of one side of the fluffed 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 one side of the cube.

We are given that the volume of the blanket is 343 cubic inches, so we can set up the equation:

343 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 343^(1/3)

s = 3

So, the length of one side of the fluffed blanket is 3 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 34B:

  Let's call the length of each side of the smaller ice cube "x".

Since the volume of the larger cube is 729 cubic cm, we can find the total number of smaller cubes by dividing the volume of the larger cube by the volume of one smaller cube.

The volume of one smaller cube is x^3, since each side has length x.

So, the total number of smaller cubes is 729 / x^3.

We know that the larger cube is a perfect cube, so it has the same length on each side. Let's call the length of one side of the larger cube "y".

Since the larger cube is made up of smaller cubes, we can find the total volume of the larger cube by multiplying the volume of one smaller cube by the number of smaller cubes.

The volume of the larger cube is y^3 = (x^3) \* (729 / x^3) = 729.

Now we have two equations:

x^3 = 729 / x^3
y^3 = 729

We can solve the first equation for x:

x^3 = 729 / x^3
x^3 \* x^3 = 729
x^6 = 729
x = 24

Now we can find y:

y^3 = 729
y = 24

So, the length of each side of the smaller ice cube is 24 cm, and the length of each side of the larger cube is also 24 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?

CodeLlama 34B:

  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 = 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 wheel is 216 cubic cm, so we can set up the equation:

216 = s^3

Now, we need to find the value of s. To do this, we can take the cube root of both sides of the equation:

s = 216^(1/3)

s = 6

So, the length of each side of the wheel is 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?

CodeLlama 34B:

  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 = s^3

where V is the volume, and s is the length of each edge.

We are given that the volume of the flower bud is 216 cubic millimeters, so we can set up the equation:

216 = s^3

Now, we can solve for s:

s = 216^(1/3)

s ≈ 6.32 millimeters

So, each edge of the flower bud is approximately 6.32 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 34B:

  To find the length of each side of the snail's cubical shell, we can use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each side.

We are given that the volume of the shell is 27 cm^3, so we can set up the equation:

27 = s^3

To find the value of s, we can take the cube root of both sides of the equation:

s = 27^(1/3)

s = 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 34B:

  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 = 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 balloon is 27 cubic feet, so we can set up the equation:

27 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 27^1/3

s = 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 34B:

  To find the length of one edge of the tank, we need to use the formula for the volume of a rectangular prism, which is:

Volume = Length x Width x Height

We know that the volume of the tank is 216 cubic feet, and we can assume that the tank is a rectangular prism with a square base. Let's call the length of one edge of the tank "x".

Then, we can set up the equation:

216 = x^3

To solve for x, we can take the cube root of both sides:

x = 216^(1/3)

x = 6

So, the length of one edge of the tank is 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?

CodeLlama 34B:

  To find the length of one side of the box, we need to use the formula for the volume of a rectangular prism, which is:

V = l × w × h

where l is the length, w is the width, and h is the height.

We are given that the volume of the box is 216 cubic inches, so we can set up the equation:

216 = l × w × h

We know that the length, width, and height are all equal, so we can simplify the equation:

216 = l × l × l

Now we can solve for l:

l = √216

l = 12

So the length of one side of the box is 12 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 34B:

  To find the length of each edge of the pocket, 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 edge.

We know that the volume of the pocket is 125 cubic inches, so we can set up the equation:

125 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 125^(1/3)

s = 5

So, the length of each edge of the pocket is 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?

CodeLlama 34B:

  Let's start by identifying the information given in the problem:

1. The total number of flowers used was 125.
2. The flowers were arranged in a cube shape.

Now, let's think about the problem:

* A cube has six faces, and each face has a length equal to the length of the other faces.
* Since the flowers are arranged in a cube shape, we can assume that each face of the cube has 25 flowers.
* The length of each side of the flower cube is equal to the number of flowers on each face.

So, the length of each side of the flower cube is 25.

### Answer: 25

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 34B:

  To find the length of a 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 a side.

We are given that the volume of one of the cucumbers is 1000 cubic centimeters, so we can set up the equation:

1000 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 10^1/3

The length of a side of the cubic cucumber is 10^1/3 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 34B:

  To find the length of one side of the cargo hold, we need to find the cube root of the volume of the hold.

The volume of the hold is given as 27 cubic meters, so we can start by finding the cube root of 27:

27^(1/3) = 3

So, the length of one side of the cargo hold is 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?

CodeLlama 34B:

  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.

We are given that the volume of the cubic cucumber is 216 cubic centimeters, so we can set up the equation:

216 = s^3

To find the value of s, we can take the cube root of both sides of the equation:

s = 216^(1/3)

s = 6

So, the length of each side of the cubic cucumber is 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)?

CodeLlama 34B:

  To find the length of one edge of the box, 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, and l is the length of one edge of the cube.

Given that the volume of the box is 729 cubic feet, 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^(1/3)

l = 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 34B:

  Yes, I can help you with that!

The number 27 corresponds to the letter "C" in the alphabet, which is the 3rd letter. To find the letter, you can use the formula:

letter = (position - 1) / 3 + 1

Plugging in the value of 27 for position, we get:

letter = (27 - 1) / 3 + 1
= 26 / 3 + 1
= 9 + 1
= 10

So, the letter that corresponds to the number 27 is "J".

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 34B:

  To find the length of each side of the buoy, we can use the formula for the volume of a rectangular prism, which is:

Volume = Length x Width x Height

Since the volume of the buoy is 1 cubic foot, we can set up the equation:

1 = Length x Width x Height

We know that the length, width, and height of the buoy are equal, so we can simplify the equation:

1 = Length^3

Taking the cube root of both sides, we get:

Length = 1^1/3 = 1

So, the length of each side of the buoy is 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?

CodeLlama 34B:

  Let's say the length of the object is x units.

We know that the temperature at the heart of the object is directly proportional to the cube of its length, so we can write:

T = k(x^3)

where T is the temperature in degrees Celsius and k is a constant.

We are also given that the temperature at the heart of the object is 729 degrees Celsius. So, we can set up the equation:

729 = k(x^3)

Now, we need to find the value of x. To do this, we can divide both sides of the equation by k:

729/k = x^3

Now, we can take the cube root of both sides of the equation:

(729/k)^(1/3) = x

So, the length of the object in units is (729/k)^(1/3).

We are not given the value of k, so we cannot find the exact length of the object. However, we can find the length of the object in terms of k.

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 34B:

  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.

We are given that the volume of the orange is 8 cubic centimeters, so we can set up the equation:

8 = s^3

To find the value of s, we can take the cube root of both sides of the equation:

s = 8^1/3

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 34B:

  To find the length of one 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 one edge of the cube.

We are given that the volume of the box is 729 cubic centimeters, so we can set up the equation:

729 = s^3

To find the length of one edge of the box, we need to take the cube root of both sides of the equation:

s = 729^(1/3)

s = 9

So, the length of one edge of the box is 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?

CodeLlama 34B:

  To find the length of one side of the compartment, we need to use the formula for the volume of a rectangular prism, which is:

Volume = Length x Width x Height

We are given that the volume of the compartment is 125 cubic inches, so we can set up the equation:

125 = Length x Width x Height

We know that the length, width, and height are all equal, so we can simplify the equation:

125 = Length^3

Now, we can take the cube root of both sides of the equation to solve for the length:

Length = 125^(1/3)

Length = 5

So, the length of one side of the compartment is 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?

CodeLlama 34B:

  To find the length of each side of the box, we can use the formula for the volume of a rectangular prism, which is:

V = lwh

where l is the length, w is the width, and h is the height.

We are given that the volume of the box is 343 cubic inches, so we can set up the equation:

343 = lwh

We know that the box is a cube, so the length, width, and height are all equal. Let's call the length of one side "s". Then we can write:

343 = s^3

Now we can solve for s:

s = 343^(1/3)

s ≈ 7.27 inches

So the length of each side of the box is approximately 7.27 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 34B:

  To find the length of each edge of the candy package, we can use the formula for the volume of a rectangular prism, which is:

V = lwh

where l is the length, w is the width, and h is the height.

We know that the volume of the candy package is 512 cubic centimeters, so we can set up an equation using this information:

512 = lwh

We also know that the package is a cube, so the length, width, and height are all equal. Let's call the length of one edge "x". Then we can write:

512 = x^3

To solve for x, we can take the cube root of both sides:

x = 512^(1/3)

x ≈ 6.48

So the length of each edge of the candy package is approximately 6.48 centimeters.

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 34B:

  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, and s is the length of a side.

We are given that the volume of the jungle gym is 512 cubic feet, so we can set up the equation:

512 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 512^(1/3)

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 34B:

  To find the length of each edge of the toothbrush, we can use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each edge.

We are given that the volume of the toothbrush is 729 cubic centimeters, so we can set up the equation:

729 = s^3

To solve for s, we can take the cube root of both sides:

s = 729^(1/3)

s ≈ 10.87

So the length of each edge of the toothbrush is approximately 10.87 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 34B:

  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 s is the length of each edge.

We are given that the volume of the star is 8 cubic light years, so we can set up the equation:

8 = s^3

Now, we need to find the cube root of 8, which is 2.

So, the length of each edge of the star is:

s = 2 light years

Therefore, 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 34B:

  To find the length of each side of the cubical chamber, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each side.

We know that the volume of the chamber is 1 unit^3, so we can set up the equation:

1 = s^3

Taking the cube root of both sides, we get:

s = 1

So, the length of each side of the cubical chamber is 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?

CodeLlama 34B:

  To find the length of each side of the cubic gadget, we need to find the cube root of the volume.

The volume of the cubic gadget is given as 1000 mm^3. To find the cube root of this number, we can use the formula:

cube root(x) = x^(1/3)

Plugging in the value of x = 1000, we get:

cube root(1000) = 1000^(1/3)

Simplifying, we get:

cube root(1000) = 10

So, the length of each side of the cubic gadget is 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?

CodeLlama 34B:

  Yes, I can help you with that!

The volume of a cube is given by the formula:

V = s^3

where s is the length of one edge of the cube.

Since the volume of the cube is 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 = 1^1/3 = 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 34B:

  To find the length of each side of the box, 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 box is 216 cubic meters, 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^(1/3)

s ≈ 6.27 meters

So, each side of the magical cube-shaped box is approximately 6.27 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 34B:

  To find the length of one side of the cube-shaped house, 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.

We are given that the volume of the house is 64 cubic feet, so we can set up the equation:

64 = s^3

To find the length of one side of the house, we need to find the cube root of 64, which is 4.

So, the length of one side of the cube-shaped house is 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?

CodeLlama 34B:

  To find the length of the edge of the toothbrush holder, we need to use the formula for the volume of a rectangular prism, which is:

Volume = Length x Width x Height

We know that the volume of the toothbrush holder is 1000 cubic centimeters, so we can set up an equation using this information:

1000 = Length x Width x Height

We also know that the length, width, and height of the toothbrush holder are equal, so we can simplify the equation:

1000 = Length^3

To solve for the length, we can take the cube root of both sides of the equation:

Length = 10^3

So, the length of the edge of the toothbrush holder is 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?

CodeLlama 34B:

  To find the length of each side of the loaf, we need to use the formula for the volume of a rectangular prism, which is:

V = lwh

where l is the length, w is the width, and h is the height.

We know that the volume of the oven is 125 cubic inches, so we can set up the equation:

125 = lwh

We also know that the bread is in a cubic form, so the length, width, and height are all equal. Let's call the length of each side "f". Then we can write:

125 = f^3

Now we can solve for f:

f = 125^(1/3)

f ≈ 5.02

So the length of each side of the loaf is approximately 5.02 inches.

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 34B:

  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.

We are given that the volume of the strawberry is 64 cubic millimeters, so we can set up the equation:

64 = s^3

To find the length of one side, we can take the cube root of both sides of the equation:

s = 64^(1/3)

s = 4

So, the length of one side of the strawberry is 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?

CodeLlama 34B:

  To find the length of each side of the rocket, 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.

Given that the volume of the rocket is 216 cubic meters, we can set up the equation:

216 = s^3

Now, we need to find the value of s. To do this, we can take the cube root of both sides of the equation:

s = 216^(1/3)

s = 6

So, the length of each side of the rocket is 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.

CodeLlama 34B:

  To find the length of one edge of the base, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the length of one edge of the cube.

We are given that the volume of the lamp base is 512 cubic inches, so we can set up the equation:

512 = s^3

Now, we can solve for s:

s = 512^(1/3)

s ≈ 15.97 inches

Therefore, the length of one edge of the lamp base is approximately 15.97 inches.

Expected answer: 8

Correct? No

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 34B:

  Let's call the length of the edge of the cube "x".

We know that the total number of eggs laid is 27, and that the eggs are arranged in a cubical shape, so the number of eggs on each face of the cube is the same.

Therefore, the number of eggs on each face of the cube is x^2.

Since there are 6 faces to the cube, the total number of eggs is 6x^2.

We are given that the total number of eggs is 27, so we can set up the equation:

6x^2 = 27

To solve for x, we can divide both sides by 6:

x^2 = 27/6

x^2 = 4

x = sqrt(4)

x = 2

Therefore, the length of the edge of the cube is 2.

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 34B:

  To find the length of one edge of the cube, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the length of one edge of the cube.

We are given that the volume of the mini school bus is 512 cubic meters, so we can set up the equation:

512 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 512^(1/3)

s ≈ 10.8 meters

Therefore, the length of one edge of the cube is approximately 10.8 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 34B:

  To find the length of each edge of the balloon, we need to use the formula for the volume of a rectangular prism, which is:

V = lwh

where l is the length, w is the width, and h is the height.

We are given that the volume of the balloon is 343 cubic meters, so we can set up the equation:

343 = lwh

We know that the balloon is a cube, so the length, width, and height are all equal. Let's call the length of one edge "x" meters. Then we can write:

343 = x^3

Now we can solve for x:

x = 343^(1/3)

x ≈ 11.8 meters

So the length of each edge of the balloon is approximately 11.8 meters.

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 34B:

  To find the length of one side of the cubic shirt design, 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.

We are given that the total volume of the shirt is 343 cubic centimeters, so we can set up the equation:

343 = s^3

To find the length of one side of the cube, we can take the cube root of both sides of the equation:

s = 343^(1/3)

s = 3.43

So the length of one side of the cubic shirt design is 3.43 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 34B:

  To find the length of each side of the roller skate container, we need to use the formula for the volume of a rectangular prism, which is:

Volume = Length x Width x Height

We know that the volume of the roller skate container is 216 cubic inches, so we can set up an equation using this information:

216 = Length x Width x Height

We also know that the length, width, and height of the roller skate container are equal, so we can simplify the equation by using the same variable (L) for each dimension:

216 = L x L x L

Now we can solve for L by dividing both sides of the equation by L:

216 = L^3

Now we can take the cube root of both sides of the equation to solve for L:

L = 216^(1/3)

L = 6

So the length of each side of the roller skate container is 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?

CodeLlama 34B:

  To find the side length of the cubic water tank, 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 side length.

We are given that the volume of the water tank is 343 cubic meters, so we can set up the equation:

343 = s^3

To find the value of s, we can take the cube root of both sides of the equation:

s = 343^(1/3)

s = 3

So, the side length of the cubic water tank is 3 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 34B:

  To find the length of each side of the backpack, we need to use the formula for the volume of a rectangular prism, which is:

Volume = Length x Width x Height

We know that the volume of the backpack is 216 cubic inches, so we can set up an equation using this formula:

216 = Length x Width x Height

We also know that the backpack has a cubical shape, which means that the length, width, and height are all equal. So, we can let Length = x, and then use this value to find the other two dimensions:

Width = x
Height = x

Now we can substitute these values into the equation we set up earlier:

216 = x x x

Simplifying this equation, we get:

216 = x^3

To find the value of x, we can take the cube root of both sides of the equation:

x = 216^(1/3)

x = 6

So, the length of each side of the backpack is 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?

CodeLlama 34B:

  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 V is the volume of the cube, and s is the length of each side.

We know that the volume of the dinosaur's brain is 1 cubic meter, so we can set up the equation:

1 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 1^1/3 = 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 34B:

  To find the edge length of the flower cube, we need to find the cube root of the volume.

The volume of the flower cube is 1000 cubic centimeters, which can be expressed as 10^3 cubic centimeters.

The cube root of 10^3 is 10, so the edge length of the flower cube is 10 centimeters.

Therefore, the edge of the flower cube is 10 centimeters long.

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 34B:

  To find the length of one side of the box, we need to divide the total volume of the box (512 cubic inches) by the number of sides of the box (6).

512 cubic inches / 6 sides = 85.333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333

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 34B:

  To find the length of each side of the toy car, 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.

Given that the volume of the toy car is 64 cubic inches, we can set up the equation:

64 = s^3

To find the length of each side, we can take the cube root of both sides of the equation:

s = 64^(1/3)

s = 4

Therefore, the length of each side of the toy car is 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?

CodeLlama 34B:

  To find the length of each side of the clock, 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.

We are given that the volume of the clock is 27 cubic inches, so we can set up the equation:

27 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 27^(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 34B:

  To find the length of a side of the cubical cargo space, we need to use the formula for the volume of a rectangular prism, which is:

V = l × w × h

where l is the length, w is the width, and h is the height.

We know that the volume of the cargo space is 8 cubic meters, so we can set up the equation:

8 = l × l × h

Now, we are given that the height and width are the same length, so we can substitute h = w:

8 = l × l × l

Now, we can solve for l:

l = √8

l = 2

So, the length of a side of the cubical cargo space is 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?

CodeLlama 34B:

  To find the length of the side of the box marked in grapes, we need to divide the total volume of the box by the volume of a single grape.

Let's assume that the grape is a perfect cube, so its volume is equal to the volume of the box. The volume of a single grape is then:

Volume of a grape = Length of a side of the grape^3

Since the box is a perfect cube, the length of the side of the box is equal to the length of the side of a grape. Therefore, we can set up the following equation:

Length of a side of the box = Length of a side of a grape

We know that the volume of the box is 343 grapes, so we can set up the following equation:

Volume of the box = Number of grapes x Volume of a grape

Volume of the box = 343 x Volume of a grape

We can solve for the volume of a grape by dividing both sides of the equation by 343:

Volume of a grape = Volume of the box / Number of grapes

Volume of a grape = 343 / 343

Volume of a grape = 1

Therefore, the length of the side of the box marked in grapes is 1.

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 34B:

  To find the length of each side of the cube, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each side.

We are given that the volume of the elephant is approximately 343 cubic meters, so we can set up the equation:

343 = s^3

To solve for s, we can take the cube root of both sides:

s = 343^(1/3)

Using a calculator, we can find that s is approximately 11.3 meters.

Therefore, the length of each side of the cube is approximately 11.3 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 34B:

  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 of the cube.

We are given that the volume of each box is 27 cubic centimeters, so we can set up the equation:

27 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 27^(1/3)

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 34B:

  To find the edge length of the territory, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the edge length of the cube.

We are given that the volume of the territory is 8 km^3, so we can set up the equation:

8 = s^3

Now, we can take the cube root of both sides of the equation to find the edge length:

s = 8^(1/3)

s = 2

So, 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 34B:

  To find the length of each side of the backpack, 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 backpack is 125 cubic inches, so we can set up the equation:

125 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 125^(1/3)

s = 5

So, the length of each side of the backpack is 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?

CodeLlama 34B:

  To find the length of each side of the cube, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each side.

We are given that the volume of the cube is 64 cubic meters, so we can set up the equation:

64 = s^3

Now, we need to find the cube root of 64, which is 4.

So, the length of each side of the cube is:

s = 4 meters

Therefore, the length of each side of the cube is 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?

CodeLlama 34B:

  To find the length of each side of the treasure chest, 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.

Given that the volume of the treasure chest is 125 cubic feet, we can set up the equation:

125 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 125^1/3

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 34B:

  To find the length of each side of the fish tank, we can use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each side.

We are given that the volume of the fish tank is 1 cubic meter, so we can set up the equation:

1 = s^3

Now, we can solve for s:

s = 1^1/3 = 1

So, the length of each side of the fish tank is 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?

CodeLlama 34B:

  To find the length of one side of the cheese 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 one side of the cube.

We are given that the volume of the cheese cube is 125 cubic centimeters, so we can set up the equation:

125 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 125^1/3

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 34B:

  To find the length of the edges of the skatepark, 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 of the cube.

We are given that the volume of the skatepark is 343 cubic meters, so we can set up the equation:

343 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 343^(1/3)

s ≈ 7.37 meters

So the length of the edges of the skatepark is approximately 7.37 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 34B:

  To find the length of a side of the box, we need to use the formula for the volume of a rectangular prism, which is:

V = lwh

where l is the length, w is the width, and h is the height. Since the volume is given as 1 cubic foot, we can set up the equation:

1 = lwh

Now, we need to find the length of one side of the box. We can do this by dividing both sides of the equation by the width and height, which are both equal to 1.

1 = l(1)(1)

l = 1

So, the length of one side of the box is 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?

CodeLlama 34B:

  To find the length of each side of the item cube, we can use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each side.

We know that the volume of the item cube is 729 cubic units, so we can set up the equation:

729 = s^3

To solve for s, we can take the cube root of both sides of the equation:

s = 729^(1/3)

s = 9

So the length of each side of the item cube is 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?

CodeLlama 34B:

  To find the length of each side of the cube, we need to use the formula for the volume of a cube, which is:

V = s^3

where s is the length of each side.

We are given that the volume of the dough is 512 cubic cm, so we can set up the equation:

512 = s^3

Now, we need to find the cube root of both sides of the equation. The cube root of 512 is 8, so:

s^3 = 8^3

s = 8

So, the length of each side of the cube is 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?

CodeLlama 34B:

  To find the length of the edge of the cubic hole, 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 of the cube.

We are given that the volume of the cubic hole is 8 cubic feet, so we can set up the equation:

8 = s^3

Now, we can solve for s:

s = 8^(1/3)

s = 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 34B:

  To determine the thickness of the string needed to produce a pitch of 343 Hz, we can use the formula:

f = (440/2^n) / (d/1000)

where f is the frequency of the note, n is the number of half-steps above the base note (A), d is the thickness of the string in millimeters, and 440 is the frequency of the base note A.

We know that the guitarist wants to play a note with a frequency of 343 Hz, so we can set up the equation:

343 = (440/2^n) / (d/1000)

We can simplify this equation by multiplying both sides by 1000 to get:

343000 = (440/2^n) / d

Now, we can solve for d by dividing both sides by 343000:

d = (440/2^n) / 343000

We know that the guitarist wants to play a note with a frequency of 343 Hz, so we can set n = 3.

Substituting n = 3 into the equation above, we get:

d = (440/2^3) / 343000

d = 1.067 mm

Therefore, the thickness of the string needed to produce a pitch of 343 Hz is approximately 1.067 millimeters.

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 34B:

  To find the length of one edge of the cubical compass box, we need to find the cube root of the cubic area.

The formula for the cube root of a number is:

cube root(x) = x^(1/3)

So, to find the length of one edge of the cubical compass box, we can use the formula:

edge length = cube root(729)

edge length = 729^(1/3)

edge length = 9

Therefore, the length of one edge of the cubical compass box is 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?

CodeLlama 34B:

  To find the side length of each page, we need to find the length of one side of the cube. We can do this by taking the cube root of the volume of one page.

The volume of one page is 64 cubic inches, so we can find the side length of one side by taking the cube root of 64:

side length = cube root(64)

The cube root of 64 is 4, so the side length of each page is 4 inches.

Expected answer: 4

Correct? Yes