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?

Llama 3 70B:

Since the sandbox is a cubic box, all sides have the same length. Let's call this length "s". The volume of the sandbox is given as 512 cubic feet, which is equal to the product of the length, width, and height of the box. Since it's a cube, the length, width, and height are all equal to "s". So, we can set up the equation:

s × s × s = 512

This is a cubic equation, and we can solve for "s" by taking the cube root of both sides:

s = ∛512

s = 8

So, the length of each side of the sandbox is 8 feet.

### Answer: 8

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?

Llama 3 70B:

Since the fireplace is a cube, all sides have the same length. Let's call the length of each side "s". The volume of a cube is given by the formula:

Volume = s × s × s = s³

We know the volume is 729 cubic feet, so we can set up the equation:

s³ = 729

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

s = ∛729
s = 9

### Answer: 9

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?

Llama 3 70B:

Since the barn is cubical, all sides have the same length. Let's call the length of each side "s". The volume of a cube is given by the formula:

Volume = s × s × s = s³

We know the volume of the barn is 1000 cubic meters, so we can set up the equation:

s³ = 1000

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

s = ∛1000
s = 10

### Answer: 10

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?

Llama 3 70B:

Reasoning: Since the tank is a cube, all sides are equal. Let's call the length of one side "s". The volume of a cube is given by V = s^3. We are given that the volume is 512 m^3, so we can set up the equation:

s^3 = 512

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

s = ∛512
s = 8

### Answer: 8

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?

Llama 3 70B:

Since the mountain has a cuboidal shape and all 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 each side.

We are given that the volume of the mountain is 64 km^3, so we can set up the equation:

s^3 = 64

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

s = ∛64
s = 4

### Answer: 4 km

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?

Llama 3 70B:

Since the crater has a cubic shape, all its edges are equal. Let's call the length of each edge "s". The volume of a cube is given by the formula:

Volume = s³

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

s³ = 512

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

s = ∛512
s = 8

### Answer: 8

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?

Llama 3 70B:

Reasoning: Since the blocks form a cube, the number of blocks is equal to the cube of the length of one side. Let's call the length of one side "x". Then, we can set up the equation:

x^3 = 343

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

x = ∛343

x = 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?

Llama 3 70B:

Reasoning: Since the container is cubic, all sides have the same length. Let's call the length of one side "s". The volume of the cube is given by V = s³. We know the volume is 512 cubic feet, so we can set up the equation:

s³ = 512

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

s = ∛512
s = 8

### Answer: 8

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?

Llama 3 70B:

Reasoning: The volume of a cube is found by cubing the edge length, i.e., Volume = Edge Length^3. 
Given that the volume of each cube is 512 mm^3, we can set up the equation: 
Edge Length^3 = 512 
To find the edge length, we take the cube root of both sides: 
Edge Length = ∛512 
Edge Length = 8 
### 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?

Llama 3 70B:

Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each side. We are given that the volume is 8 cubic cm, so we can set up the equation:

s^3 = 8

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

s = ∛8
s = 2

### Answer: 2

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?

Llama 3 70B:

Reasoning: Since the volume of the cube is 27 cubic kilometers, we can set up the equation:

Volume = s^3
27 = s^3

where s is the length of one edge of the cube. To find the value of s, we take the cube root of both sides of the equation:

s = ∛27
s = 3

### Answer: 3

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?

Llama 3 70B:

Since the volume of the box is 1 cubic inch, and the box is a cube, we can set up the equation:

side × side × side = 1

where "side" is the length of each side of the box.

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

side = ∛1
side = 1

So, the length of each side of the box is 1 inch.

### Answer: 1

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?

Llama 3 70B:

Let's break this problem down step by step!

Since each cubic centimeter of the flower holds 1 milliliter of nectar, and the flower holds 125 milliliters of nectar, we can set up the following equation:

Volume of the cube (in cubic centimeters) = 125

Since the flower grows in the shape of a cube, the volume of the cube is given by:

Volume = side^3

where "side" is the length of one side of the cube.

Equating the two expressions, we get:

side^3 = 125

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

side = ∛125
side = 5

### Answer: 5

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?

Llama 3 70B:

Reasoning: Since the tree stump is cubical, all sides are equal. Let's call the length of one side "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the side length.

We are given that the volume V = 125 cubic meters. To find the side length, we can take the cube root of both sides of the equation:

s³ = 125
s = ∛125
s = 5

### 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?

Llama 3 70B:

Reasoning: The formula to find the volume of a cube is V = s³, where V is the volume and s is the length of each edge. We are given that the volume is 1000 cubic millimeters, so we can set up the equation:

1000 = s³

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

s = ∛1000
s = 10

So, the length of each edge of the bracelet is 10 millimeters.

### Answer: 10

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?

Llama 3 70B:

Since the soap is in the shape of a cube, all sides are equal. Let's call the length of each side "s". 

The volume of a cube is given by the formula: Volume = s × s × s = s³

We know the volume is 1 cubic cm, so we can set up the equation: s³ = 1

To find the length of each side, we take the cube root of both sides: s = ∛1 = 1

### Answer: 1

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?

Llama 3 70B:

Since the tree is cubic, all its edges are equal. Let's call the length of each edge "x". The volume of a cube is given by the formula V = x³, where V is the volume and x is the length of each edge.

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

x³ = 216

To find the length of each edge, we need to find the cube root of 216:

x = ∛216
x = 6

### Answer: 6

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?

Llama 3 70B:

Reasoning: Since the blanket is folded into a perfect cube shape, all sides have the same length. Let's call the length of each side "s". The volume of a cube is given by the formula V = s³, where V is the volume and 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:

s³ = 1000

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

s = ∛1000
s = 10

### Answer: 10

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?

Llama 3 70B:

Reasoning: Since the box is a cube, all sides have the same length. Let's call the length of each side "s". The volume of the cube is given by the formula: Volume = s × s × s = s³. We know the volume is 125 cubic centimeters, so we can set up the equation: s³ = 125. To find the length of each side, we take the cube root of both sides: s = ∛125 = 5. 
### Answer: 5

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?

Llama 3 70B:

Since the perfume bottle is shaped like a cube, all its sides are equal. Let's call the length of each side "s". 

The volume of a cube is given by the formula: Volume = s × s × s = s³

We know the volume of the perfume bottle is 125 cubic centimeters, so we can set up the equation:

s³ = 125

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

s = ∛125
s = 5

### Answer: 5

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?

Llama 3 70B:

Let's call the length of one side of the cuboidal structure "s". Since the height, width, and depth are all equal, the volume of the building can be calculated as:

Volume = s × s × s = s³

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

s³ = 216

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

s = ∛216
s = 6

### Answer: 6

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?

Llama 3 70B:

Since the chair is in the shape of a cube, all sides are equal. Let's call the length of each side "s". The volume of a cube is given by the formula:

Volume = s × s × s = s³

We are given that the volume is 343 cubic feet. So, we can set up the equation:

s³ = 343

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

s = ∛343
s = 7

### Answer: 7

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?

Llama 3 70B:

Reasoning: The volume of a cube is given by the formula V = s^3, where 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 find the length of a side of the cube, we take the cube root of both sides of the equation:

s = ∛729
s = 9

### Answer: 9

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?

Llama 3 70B:

Reasoning: Since the spaceship is a cube, all its edges are equal. Let's call the length of each edge "s". The volume of a cube is given by the formula V = s³, where V is the volume and 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:

s³ = 8

To find the length of each edge, we need to find the cube root of 8:

s = ∛8
s = 2

### Answer: 2

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?

Llama 3 70B:

Reasoning: Since the storage unit is a cube, all sides have the same length. Let's call the length of each side "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of each side.

We are given that the volume V is 343 cubic feet. We can set up the equation:

s³ = 343

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

s = ∛343

s = 7

### Answer: 7

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?

Llama 3 70B:

Reasoning: The formula to find the volume of a cube is V = s³, where V is the volume and s is the length of the edge. 
We are given that the volume is 8 cubic inches, so we can set up the equation: 8 = s³.
To find the length of the edge, we take the cube root of both sides: s = ∛8.
s = 2, since 2³ = 8.
### Answer: 2

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?

Llama 3 70B:

Since the plot is a cube, all sides have the same length. Let's call the length of each side "s". Then, the volume of the cube is s × s × s = s³.

We know the volume is 729 cubic meters, so we can set up the equation:

s³ = 729

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

s = ∛729

s = 9

So, the length of each side of the plot is 9 meters.

### Answer: 9

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?

Llama 3 70B:

Reasoning: Since the slide has a cuboid shape with the same length, width, and height, it is a cube. The volume of a cube is given by V = s^3, where s is the length of one side. We are given that the volume is 1000 cubic feet, so we can set up the equation:

s^3 = 1000

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

s = ∛1000
s = 10

### Answer: 10

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?

Llama 3 70B:

Reasoning: Since the volume of the cube is 512 cubic feet, and the volume of a cube is given by the formula V = s^3, where s is the length of each side, we can set up the equation:

s^3 = 512

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

s = ∛512

s = 8

### Answer: 8

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?

Llama 3 70B:

Reasoning: Since the hat is a perfect cube, all its edges are equal. Let's call the length of one edge "x". The volume of a cube is given by the formula V = x³, where V is the volume and x is the length of one edge.

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

x³ = 27

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

x = ∛27
x = 3

### Answer: 3

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?

Llama 3 70B:

Reasoning: Since the container is cube-shaped, each side of the cube has the same length. Let's call this length "x". The volume of the cube is x × x × x = x³. We know that the container holds 27 grapes, so the volume of the cube is equal to 27. Therefore, we can set up the equation x³ = 27.

To solve for x, we take the cube root of both sides of the equation: x = ∛27. Since 3 × 3 × 3 = 27, we know that x = 3.

So, each side of the cube holds 3 grapes.
### Answer: 3

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?

Llama 3 70B:

Reasoning: Since the container is a cube, all sides have the same length. Let's call the length of one side "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the side length.

We know the volume V = 216 cubic meters, so we can set up the equation:

s³ = 216

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

s = ∛216

s = 6

### Answer: 6

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?

Llama 3 70B:

Since the charm is a cube, all its edges are equal. Let's call the length of each edge "s". The volume of a cube is given by the formula V = s³.

We know the volume of the charm is 64 mm³, so we can set up the equation:

s³ = 64

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

s = ∛64
s = 4

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

### Answer: 4

Expected answer: 4

Correct? Yes

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

Llama 3 70B:

Reasoning: If a number is cubed and the result is 64, that means we need to find the number that, when multiplied by itself three times, gives us 64.

Let's call the number "x". Then, we can write the equation as:

x × x × x = 64

This can be rewritten as:

x³ = 64

To find the value of x, we need to find the cube root of 64. The cube root of 64 is 4, because 4 × 4 × 4 = 64.

### 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?

Llama 3 70B:

Since the mug has a cubic shape, each side has the same length. Let's call the length of each side "s". Since the volume of the mug is 1 liter, we can set up the equation:

s × s × s = 1

Since s is the length of each side, we can take the cube root of both sides of the equation to solve for s:

s = ∛1
s = 1

So, each side of the petite mug is 1 liter long.

### Answer: 1

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?

Llama 3 70B:

Reasoning: The volume of a cube is found by cubing the length of one side (V = s^3). We are given the volume, so we can set up the equation: 343 = s^3. To find the length of one side, we take the cube root of both sides: s = ∛343. Since 7^3 = 343, we know that ∛343 = 7.
### Answer: 7

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?

Llama 3 70B:

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 set up the equation:

x^3 = 729

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

x = ∛729

x = 9

So, the length of each side of the smaller ice cube is 9 cm.

### Answer: 9

Expected answer: 9

Correct? Yes

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?

Llama 3 70B:

Since the wheel has a cubic shape, all sides are equal. Let's call the length of each side "s". The volume of a cube is given by the formula:

Volume = s × s × s = s³

We know the volume is 216 cubic cm, so we can set up the equation:

s³ = 216

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

s = ∛216

s = 6

### Answer: 6

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?

Llama 3 70B:

Reasoning: Since the flower bud is cubic, all its edges are equal. Let's call the length of each edge "s". Then, the volume of the bud is s × s × s = s³. We know the volume is 216 cubic millimeters, so we can set up the equation:

s³ = 216

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

s = ∛216
s = 6

### Answer: 6

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?

Llama 3 70B:

Reasoning: Since the shell is a cube, all sides have the same length. Let's call the length of each side "s". The volume of a cube is given by the formula V = s^3. We know the volume is 27 cm^3, so we can set up the equation:

s^3 = 27

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

s = ∛27
s = 3

### Answer: 3

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?

Llama 3 70B:

Reasoning: Since the balloon is a cube, all sides are equal. Let's call the length of one side "s". The volume of a cube is given by the formula V = s³. We know the volume is 27 cubic feet, so we can set up the equation:

s³ = 27

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

s = ∛27
s = 3

### Answer: 3

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?

Llama 3 70B:

Since the tank is cubic, all its edges are equal. Let's call the length of one edge "x". Then, the volume of the tank is x × x × x = x³.

We know the volume of the tank is 216 cubic feet, so we can set up the equation:

x³ = 216

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

x = ∛216

x = 6

### Answer: 6

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?

Llama 3 70B:

Since the box is cube-shaped, all sides have the same length. Let's call the length of one side "s". The volume of a cube is given by the formula:

Volume = s × s × s = s³

We know the volume is 216 cubic inches, so we can set up the equation:

s³ = 216

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

s = ∛216

s = 6

### Answer: 6

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?

Llama 3 70B:

Let's call the length of each edge of the cube "s". Since it's a cube, all edges have the same length.

The volume of a cube is given by the formula: Volume = s³

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

s³ = 125

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

s = ∛125
s = 5

### Answer: 5

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?

Llama 3 70B:

Reasoning: Since the flowers are arranged in a cube shape, the number of flowers is equal to the cube of the length of each side. Let's call the length of each side "x". Then, we can set up the equation:

x^3 = 125

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

x = ∛125
x = 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?

Llama 3 70B:

Reasoning: Since the cucumber is a perfect cube, all its sides are equal. Let's call the length of a side "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of a side.

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

s³ = 1000

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

s = ∛1000
s = 10

### Answer: 10

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?

Llama 3 70B:

Since all sides of the cargo hold have 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. We are given that the volume is 27 cubic meters, so we can set up the equation:

s^3 = 27

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

s = ∛27
s = 3

### Answer: 3

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?

Llama 3 70B:

Reasoning: Since the cucumber is a perfect cube, all sides have the same length. Let's call this length "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of a side.

We are given that the volume V is 216 cubic centimeters. We can set up the equation:

216 = s³

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

s = ∛216

s = 6

So, the length of each side of the cubic cucumber is 6 centimeters.

### Answer: 6

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)?

Llama 3 70B:

Reasoning: Since the box is cubic, all edges have the same length. Let's call the length of one edge "x". The volume of a cube is given by the formula V = x³, where V is the volume and x is the length of one edge.

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

x³ = 729

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

x = ∛729
x = 9

### Answer: 9

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.)

Llama 3 70B:

Let's think about it! If the number 27 corresponds to a letter's position in the alphabet cubed, that means we need to find a number that, when cubed, gives us 27.

Let's try to find the cube root of 27:

³√27 = 3

So, the number that, when cubed, gives us 27 is 3. Now, we need to find the letter that corresponds to the position 3 in the alphabet.

Using the standard ordering of the alphabet, we get:

a = 1, b = 2, c = 3

So, the letter 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?

Llama 3 70B:

Since the buoy is cubical, all sides have the same length. Let's call the length of each side "s". The volume of a cube is given by the formula:

Volume = s × s × s = s³

We know the volume of the buoy is 1 cubic foot, so we can set up the equation:

s³ = 1

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

s = ∛1
s = 1

So, the length of each side of the buoy is 1 foot.

### Answer: 1

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?

Llama 3 70B:

Let's call the length of the object "x". Since the temperature is directly proportional to the cube of its length, we can write an equation:

Temperature = k × x³

where k is the proportionality constant.

We are given that the temperature is 729 degrees, so we can plug this value into the equation:

729 = k × x³

To solve for x, we can start by noticing that 729 is a perfect cube: 729 = 9³. So, we can rewrite the equation as:

9³ = k × x³

Now, we can equate the cubes:

9 = x

So, 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?

Llama 3 70B:

Reasoning: Since the orange is a cube, all sides are equal. Let's call the length of each side "s". The volume of a cube is given by the formula V = s³. We know the volume is 8 cubic centimeters, so we can set up the equation:

s³ = 8

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

s = ∛8
s = 2

### Answer: 2

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?

Llama 3 70B:

Reasoning: Since the mirror box is cubical, all its edges are equal. Let's call the length of one edge "x". The volume of a cube is given by the formula V = x³, where V is the volume and x is the length of one edge.

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

x³ = 729

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

x = ∛729
x = 9

### Answer: 9

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?

Llama 3 70B:

Reasoning: Since the storage compartment is cubical, all sides have the same length. Let's call this length "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of one side.

We are given that the volume V is 125 cubic inches. We can set up the equation:

s³ = 125

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

s = ∛125
s = 5

### Answer: 5

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?

Llama 3 70B:

Reasoning: Since the box is cube-shaped, all sides have the same length. Let's call this length "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of a side.

We are given that the volume V is 343 cubic inches. We can set up an equation:

s³ = 343

To find the length of a side, we take the cube root of both sides:

s = ∛343

s = 7

### Answer: 7

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?

Llama 3 70B:

Reasoning: Since the package is a cube, all its edges are equal. Let's call the length of each edge "s". The volume of a cube is given by the formula V = s³. We know the volume is 512 cubic centimeters, so we can set up the equation:

s³ = 512

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

s = ∛512
s = 8

So, each edge of the candy package is 8 centimeters long.

### Answer: 8

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?

Llama 3 70B:

Reasoning: Since the jungle gym is a cube, all sides are equal. Let's call the length of a side "s". The volume of a cube is given by the formula V = s³. We know the volume is 512 cubic feet, so we can set up the equation:

s³ = 512

To find the length of a side, we take the cube root of both sides:

s = ∛512
s = 8

### Answer: 8

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?

Llama 3 70B:

Since the toothbrush is a perfect cube, all its edges are equal. Let's call the length of each edge "x". 

The volume of a cube is given by the formula: Volume = x³ 

We know the volume is 729 cubic centimeters, so we can set up the equation: x³ = 729 

To find the value of x, we take the cube root of both sides: x = ∛729 

x = 9 

### Answer: 9

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)?

Llama 3 70B:

Since the star is a perfect cube, all its edges are equal. Let's call the length of each edge "s". 

The volume of a cube is given by the formula: Volume = s³ 

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

s³ = 8 

To find the length of each edge, we need to find the cube root of 8: 

s = ∛8 
s = 2 

### Answer: 2

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?

Llama 3 70B:

Since the chamber is cubical, all sides have the same length. Let's call this length "s". The volume of the cubical chamber is s × s × s = s³.

We know that the volume of the chamber is equal to the intensity of the dolphin's call, which is 1 unit³. Therefore, we can set up the equation:

s³ = 1

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

s = ∛1
s = 1

### Answer: 1

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?

Llama 3 70B:

Reasoning: Since the gadget is a cube, all sides are equal. Let's call the length of each side "s". The volume of a cube is given by the formula: Volume = s × s × s = s³.

We are given that the volume is 1000 mm³, so we can set up the equation: s³ = 1000.

To find the length of each side, we take the cube root of both sides of the equation: s = ∛1000 = 10.

### 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?

Llama 3 70B:

Reasoning: The formula to find the volume of a cube is V = s³, where V is the volume and s is the length of one edge. We are given that the volume is 1 cubic meter, so we can set up the equation:

1 = s³

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

s = ∛1
s = 1

### Answer: 1

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?

Llama 3 70B:

Reasoning: Since the box is cube-shaped, all sides are equal. Let's call the length of each side "s". The volume of a cube is given by the formula: Volume = s × s × s = s³. We know the volume is 216 cubic meters, so we can set up the equation: s³ = 216. To find the value of s, we take the cube root of both sides: s = ∛216 = 6. 
### Answer: 6

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?

Llama 3 70B:

Reasoning: Since the house is cube-shaped, all sides have the same length. Let's call the length of one side "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of one side.

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

s³ = 64

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

s = ∛64
s = 4

### Answer: 4

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?

Llama 3 70B:

Reasoning: Since the toothbrush holder is cubical, all its edges are equal. Let's call the length of one edge "x". The volume of a cube is given by the formula V = x³, where V is the volume and x is the length of one edge.

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

x³ = 1000

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

x = ∛1000
x = 10

### Answer: 10

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?

Llama 3 70B:

Since the oven is in a cubic shape, its volume can be represented as V = s^3, where s is the length of each side. We are given that the volume of the oven is 125 cubic inches, so we can set up the equation:

125 = s^3

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

s = ∛125
s = 5

So, the length of each side of the loaf (f) is 5 inches.

### Answer: 5

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?

Llama 3 70B:

Reasoning: Since the strawberry is a cube, all its sides are equal. Let's call the length of one side "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the side length.

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

64 = s³

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

s = ∛64
s = 4

### Answer: 4

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?

Llama 3 70B:

Reasoning: Since the rocket is a perfect cube, all sides have the same length. Let's call the length of each side "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of each side.

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

s³ = 216

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

s = ∛216
s = 6

### Answer: 6

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.

Llama 3 70B:

Reasoning: Since the lamp base is a cube, all its edges are equal. Let's call the length of one edge "x". The volume of a cube is given by the formula V = x³, where V is the volume and x is the length of one edge.

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

x³ = 512

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

x = ∛512
x = 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?

Llama 3 70B:

Reasoning: Since the eggs are arranged in a cubical shape, the number of eggs can be represented as the cube of an integer. In this case, 27 is a perfect cube, specifically 3^3. Therefore, the length of the edge of the cube is 3.
### Answer: 3

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'?

Llama 3 70B:

Reasoning: Since the shape of the bus can be closely approximated as a cube, we can find the length of one edge by taking the cube root of the volume.

Let's denote the length of one edge as x. Then, the volume of the cube is x³.

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

x³ = 512

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

x = ∛512
x = 8

### Answer: 8

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?

Llama 3 70B:

Since the balloon is a cube, all its edges are equal. Let's call the length of each edge "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of each edge.

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

s³ = 343

To find the length of each edge, we need to find the cube root of 343. We can do this by asking ourselves, "What number multiplied by itself three times gives us 343?"

The answer is 7, since 7 × 7 × 7 = 343.

So, the length of each edge of the balloon is 7 meters.

### Answer: 7

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?

Llama 3 70B:

Reasoning: Since the shirt is a 3D cube design, all sides are equal. The formula to find the volume of a cube is V = s³, where V is the volume and s is the length of one side. We are given the volume, 343 cubic centimeters. To find the length of one side, we take the cube root of the volume: s = ∛V = ∛343 = 7.
### Answer: 7

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?

Llama 3 70B:

Since the roller skate container is a cube, all its sides are equal. Let's call the length of each side "s". 

The volume of a cube is given by the formula: Volume = s × s × s = s³

We know the volume is 216 cubic inches, so we can set up the equation: s³ = 216

To find the value of s, we take the cube root of both sides: s = ∛216

s = 6

### Answer: 6

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?

Llama 3 70B:

Since the tank is cubic, all sides have the same length. Let's call this length "s". The volume of the tank is given by the formula:

Volume = s × s × s = s³

We know the volume is 343 cubic meters, so we can set up the equation:

s³ = 343

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

s = ∛343

s = 7

### Answer: 7

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?

Llama 3 70B:

Since the backpack has a cubical shape, all sides are equal. Let's call the length of each side "s". The volume of a cube is given by the formula:

Volume = s × s × s = s³

We know the volume of the backpack is 216 cubic inches, so we can set up the equation:

s³ = 216

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

s = ∛216
s = 6

### Answer: 6

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?

Llama 3 70B:

Reasoning: Since the brain is cube-shaped, all sides have the same length. Let's call the length of each side "s". The volume of a cube is given by the formula: Volume = s × s × s = s³. We know the volume is 1 cubic meter, so we can set up the equation: s³ = 1. To find the length of each side, we take the cube root of both sides: s = ∛1 = 1. 
### Answer: 1

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?

Llama 3 70B:

Reasoning: Since the cluster of flowers is a perfect cube, all its edges are equal. Let's call the length of one edge "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of one edge.

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

s³ = 1000

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

s = ∛1000
s = 10

### Answer: 10

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?

Llama 3 70B:

Reasoning: Since the box is cube-shaped, all sides have the same length. Let's call the length of one side "s". The volume of the box is given by the formula: Volume = s × s × s = s³. We know the volume is 512 cubic inches, so we can set up the equation: s³ = 512. To find the value of s, we take the cube root of both sides: s = ∛512 = 8. 
### Answer: 8

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?

Llama 3 70B:

Reasoning: Since the toy car is a cube, all sides are equal. Let's call the length of each side "s". The volume of a cube is given by the formula V = s³. We know the volume is 64 cubic inches, so we can set up the equation:

s³ = 64

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

s = ∛64
s = 4

### Answer: 4

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?

Llama 3 70B:

Since the clock is cube-shaped, all sides have the same length. Let's call the length of each side "s". 

The volume of a cube is given by the formula: Volume = s × s × s = s³

We know the volume of the clock is 27 cubic inches, so we can set up the equation: s³ = 27

To find the length of each side, we take the cube root of both sides of the equation: s = ∛27

s = 3

### Answer: 3

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?

Llama 3 70B:

Let's call the length, width, and height of the cuboidal trailer "s". Since the volume of the cargo space is 8 cubic meters, we can set up the equation:

s × s × s = 8

Since the height and width are the same length, we can simplify the equation to:

s³ = 8

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

s = ∛8
s = 2

So, the length of a side of the cubical cargo space is 2 meters.

### Answer: 2

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?

Llama 3 70B:

Reasoning: Since the box is cubic, all sides have the same length. Let's call the length of one side "x". Since the box perfectly fits 343 grapes, the volume of the box is equal to 343. The volume of a cube is given by the formula V = x^3, where x is the length of one side. Therefore, we can set up the equation x^3 = 343. To solve for x, we take the cube root of both sides: x = ∛343 = 7.

### Answer: 7

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?

Llama 3 70B:

Reasoning: Since the elephant has a perfect cube shape, the volume of the elephant can be represented as V = s^3, where s is the length of each side. We are given that the volume is approximately 343 cubic meters, so we can set up the equation:

343 = s^3

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

s = ∛343
s = 7

### Answer: 7

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.

Llama 3 70B:

Reasoning: Since the box is a cube, all its edges are equal. Let's call the length of an edge "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of an edge.

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

s³ = 27

To find the length of an edge, we need to find the cube root of 27:

s = ∛27
s = 3

### Answer: 3

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?

Llama 3 70B:

Reasoning: Since the territory is cube-shaped, all its edges are equal. Let's call the edge length "s". The volume of a cube is given by the formula V = s^3, where V is the volume and s is the edge length.

We are given that the volume V = 8 km^3. We can set up the equation:

s^3 = 8

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

s = ∛8
s = 2

### Answer: 2

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?

Llama 3 70B:

Since the backpack is a cube, all sides have the same length. Let's call the length of each side "s". The volume of a cube is given by the formula:

Volume = s × s × s = s³

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

s³ = 125

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

s = ∛125
s = 5

### Answer: 5

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?

Llama 3 70B:

Reasoning: The formula to find the volume of a cube is V = s³, where V is the volume and s is the length of each side. We are given that the volume is 64 cubic meters, so we can set up the equation:

64 = s³

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

s = ∛64
s = 4

So, the length of each side of the cube is 4 meters.

### Answer: 4

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?

Llama 3 70B:

Reasoning: Since the treasure chest has a cube shape, all sides are equal. Let's call the length of each side "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of each side.

We are given that the volume of the treasure chest is 125 cubic feet, so we can set up the equation:

s³ = 125

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

s = ∛125
s = 5

### Answer: 5

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?

Llama 3 70B:

Since the fish tank is a cube, all sides have the same length. Let's call the length of each side "s". The volume of the cube is given by the formula:

Volume = s × s × s = s³

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

s³ = 1

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

s = ∛1
s = 1

So, the length of each side of the fish tank is 1 meter.

### Answer: 1

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?

Llama 3 70B:

Reasoning: Since the appetizer is a cube, all sides are equal. Let's call the length of one side "s". The volume of a cube is given by the formula: Volume = s × s × s = s³. We know the volume is 125 cubic centimeters, so we can set up the equation: s³ = 125. To find the length of one side, we take the cube root of both sides: s = ∛125 = 5. 
### Answer: 5

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?

Llama 3 70B:

Reasoning: Since the skatepark is a perfect cube, all its edges have the same length. Let's call this length "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of an edge. We are given that the volume is 343 cubic meters, so we can set up the equation:

s³ = 343

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

s = ∛343

s = 7

### Answer: 7

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?

Llama 3 70B:

Reasoning: Since the box is cubical, all sides have the same length. Let's call the length of a side "s". The volume of the box is given by V = s × s × s = s³. We know that the volume is 1 cubic foot, so we can set up the equation: s³ = 1. To find the length of a side, we take the cube root of both sides: s = ∛1 = 1. 
### Answer: 1

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?

Llama 3 70B:

Reasoning: Since the volume of the cube is 729 cubic units, we can find the length of each side by taking the cube root of the volume.

Let's denote the length of each side as x. Then, the volume of the cube is x³ = 729.

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

x = ∛729
x = 9

So, the length of each side of the item cube is 9 units.

### Answer: 9

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?

Llama 3 70B:

Reasoning: Since the cookie dough is in the shape of a cube, all sides have the same length. Let's call the length of each side "s". The volume of a cube is given by the formula V = s³, where V is the volume and s is the length of each side.

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

512 = s³

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

s = ∛512
s = 8

### Answer: 8

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?

Llama 3 70B:

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

s^3 = 8

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

s = ∛8
s = 2

### Answer: 2

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?

Llama 3 70B:

Let's call the thickness of the string "x" in hundreds of a millimeter. Since the pitch is determined by the cube of the thickness, we can set up the equation:

x^3 = 343

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

x = ∛343

x = 7

So, the thickness of the string the guitarist should choose is 7 hundredths of a millimeter.

### Answer: 7 hundredths of a millimeter.

Expected answer: 7

Correct? Yes

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?

Llama 3 70B:

Reasoning: Since the compass box is a cube, all its edges are equal. Let's call the length of one edge "x". Then, the volume of the cube is x × x × x = x³. We are given that the volume is 729 cubic cm, so we can set up the equation:

x³ = 729

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

x = ∛729
x = 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?

Llama 3 70B:

Since the page is in the shape of a cube, all its sides are equal. Let's call the side length "s". The volume of a cube is given by the formula:

Volume = s × s × s = s³

We know the volume of one page is 64 cubic inches, so we can set up the equation:

s³ = 64

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

s = ∛64
s = 4

### Answer: 4 inches

Expected answer: 4

Correct? Yes