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 8B:

Reasoning: Since the sandbox is a cubic box, all sides have the same length. Let's call this length "x". The volume of the sandbox is given as 512 cubic feet, which is equal to x^3.

We can set up the equation: x^3 = 512

To solve for x, we can take the cube root of both sides: x = ∛512

Using a calculator, we get: x ≈ 8.00

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

### Answer: 8.00

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 8B:

Reasoning: The volume of a cube is found by multiplying the length of each side cubed (length × width × height). Since the volume is given as 729 cubic feet, we can set up the equation:

length × width × height = 729

Since it's a cube, all sides are equal, so we can let the length, width, and height be represented by the variable "x". Then, the equation becomes:

x × x × x = 729

Simplifying the equation, we get:

x³ = 729

Taking the cube root of both sides, we get:

x = ∛729

x = 9

So, the length of each side of the fireplace is 9 feet.

### 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 8B:

Reasoning: Since the barn is a cube, its volume is equal to the length of one side squared, multiplied by itself. We can set up an equation based on this:

side^3 = 1000

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

side = ∛1000

side = 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 8B:

Reasoning: Since the tank is a cube, its volume is equal to the cube of its side length. We can set up an equation using the formula for the volume of a cube (V = s^3), where V is the volume and s is the side length.

512 = s^3

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

s = ∛512

Using a calculator, we get:

s ≈ 8.07

So, the size of one side of the tank is approximately 8.07 meters.

### Answer: 8.07

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?

Llama 3 8B:

Reasoning: The volume of a cuboid is given by the formula V = l × w × h, where l, w, and h are the length, width, and height of the cuboid, respectively. Since the sides of the cuboid are of equal length, we can let l = w = h = x. Then, the volume equation becomes V = x × x × x = x^3.

Given that the volume is 64 km^3, we can set up the equation x^3 = 64 and solve for x.

x^3 = 64
x = ∛64
x = 4

So, the length of each side of the cuboid is 4 kilometers.

### Answer: 4

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 8B:

Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each edge. We are given that the volume is 512 cubic kilometers, 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

Using a calculator, we get:

s ≈ 8.0

So, the length of each edge of the crater is approximately 8.0 kilometers.

### Answer: 8.0

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 8B:

Reasoning: Since the baby is building a cube, the total number of blocks is equal to the cube of the length of one side. We can set up the equation:

343 = x^3

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

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

x = ∛343

x = 7

So, the length of one side of the cube is 7 blocks.

### 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 8B:

Reasoning: Since the substance is in a cubic container, the volume of the substance is equal to the length of one side of the container cubed. In other words, the volume is equal to the length × length × length.

Let's call the length of one side of the container "x". Then, the volume of the substance is x × x × x = x³.

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

x³ = 512

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

x = ∛512

x = 8

So, the length of one side of the cubic container is 8 feet.

### 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 8B:

Reasoning: The volume of a cube is found by cubing the edge length. In this case, the volume is 512 mm^3, so 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

Using a calculator, we get:

edge length = 8 mm

### Answer: 8 mm

Expected answer: 8

Correct? Yes

Problem: The letter G in a certain font uses a cube as a model for its design. If the volume of this cubic model is 8 cubic cm, what is the length of each side of the cube in cm?

Llama 3 8B:

Reasoning: The volume of a cube is found by cubing the length of one side. In this case, the volume is 8 cubic cm, so we can set up the equation:

side^3 = 8

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

side = ∛8

side = 2

So, the length of each side of the cube is 2 cm.

### 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 8B:

Reasoning: The volume of a cube is calculated by multiplying the length of one edge by itself three times (length × width × height = volume). Since the volume of the shark's territory is 27 cubic kilometers, we can set up the equation:

length × length × length = 27

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

length = ∛27

Using a calculator, we get:

length = 3 kilometers

### 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 8B:

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

side × side × side = 1

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

side = ∛1

side = 1

### 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 8B:

Reasoning: Let's say the length of one side of the cube is x centimeters. Then, the volume of the cube is x^3 cubic centimeters.
Since each cubic centimeter holds 1 milliliter of nectar, the total volume of the cube in milliliters is x^3 cubic centimeters * 1 milliliter/cubic centimeter = x^3 milliliters.
We know that the total volume of the cube is 125 milliliters, so we can set up the equation x^3 = 125.
Taking the cube root of both sides, we get x = ∛125 = 3.57 (approximately).
Since the length of one side of the cube must be a whole number of centimeters, we round down to the nearest whole number, which is 3 centimeters.
### Answer: 3

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?

Llama 3 8B:

Reasoning: Since the tree stump is a cube, its volume is equal to the length of one side squared, multiplied by itself. We can set up the equation:

side^3 = 125

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

side = ∛125

side = 5

### Answer: 5

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 8B:

Reasoning: The volume of a cube is given by the formula V = s^3, where 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 = s^3

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

s = ∛1000

Using a calculator, we get:

s ≈ 10

So, the length of each edge of the bracelet is approximately 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 8B:

Reasoning: The volume of a cube is found by cubing the length of one side. In this case, the volume is 1 cubic cm, so we can set up the equation:

side^3 = 1

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

side = ∛1

side = 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 8B:

Reasoning: The volume of a cube is found by multiplying the length of each edge by itself three times (length × width × height = volume). Since the volume of the yew tree is 216 cubic meters, we can set up the equation:

edge × edge × edge = 216

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

edge = ∛216

Using a calculator, we get:

edge = 6

So, the length of each edge of the yew tree is 6 meters.

### 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 8B:

Reasoning: Since the blanket is folded in a perfect cube shape, all sides are equal. Let's call the length of each side "x". The volume of a cube is calculated by multiplying the length of each side cubed (x^3). In this case, the volume is 1000 cubic cm, so we can set up the equation:

x^3 = 1000

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

x = ∛1000

x ≈ 10

So, the length of each side of the blanket is approximately 10 centimeters.

### 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 8B:

Reasoning: Since the box is a cube, all its sides have the same length. Let's call this length "x". The volume of a cube is found by cubing its side length, so we can set up the equation:

x × x × x = 125

This is a cubic equation, and we can simplify it by taking the cube root of both sides:

x³ = 125

x = ∛125

x = 5

So, the length of each side of the box is 5 centimeters.

### 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 8B:

Reasoning: Since the perfume bottle is a cube, its volume is equal to the length of its side squared, multiplied by itself. We can set up the equation:

side^3 = 125

To find the length of the side, we need to find the cube root of 125. This can be done using a calculator or by finding the perfect cube of a number that is close to 125.

125 = 5^3

So, the length of each side of the bottle is 5 centimeters.

### 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 8B:

Reasoning: Since the building has a uniform cross-sectional area, the area of the cross-section is equal to the width times the depth. Let's call the width and depth "x". Then, the area of the cross-section is x^2.

The volume of the building is the area of the cross-section multiplied by the height. Since the height, width, and depth are all equal, let's call the height "x" as well. Then, the volume is x^2 * x = x^3.

We know the volume is 216 cubic meters, so we can set up the equation x^3 = 216. Taking the cube root of both sides, we get x = ∛216 = 6.

So, the length of one side is 6 meters.

### 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 8B:

Reasoning: The volume of a cube is found by cubing the length of its side. So, if the volume is 343 cubic feet, we can set up the equation:

side^3 = 343

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

side = ∛343

side = 7

So, the length of each side of the chair is 7 feet.

### 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 8B:

Reasoning: The volume of a cube is calculated by cubing the length of a side. In this case, the volume is 729 cubic inches, so we can set up the equation:

side^3 = 729

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

side = ∛729

Using a calculator, we find that:

side = 9

So, the length of a side of each cube is 9 inches.
### 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 8B:

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

8 = s^3

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

s = ∛8

Using a calculator, we get:

s ≈ 2.08 miles

So, the length of each edge of the spaceship is approximately 2.08 miles.

### Answer: 2.08

Expected answer: 2

Correct? No

Problem: A strawberry farmer builds a cube-shaped cold storage unit for his strawberries. The cold storage has a volume of 343 cubic feet. What is the length of each side of the storage unit in feet?

Llama 3 8B:

Reasoning: Since the cold storage unit is a cube, all its sides have the same length. Let's call this length "x". The volume of a cube is found by cubing its side length, so we can set up the equation:

x^3 = 343

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

x = ∛343

x = 7

So, the length of each side of the cold storage unit is 7 feet.

### 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 8B:

Reasoning: The volume of a cube is found by cubing the length of its edge. So, if the volume is 8 cubic inches, we can set up the equation:

edge^3 = 8

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

edge = ∛8

Using a calculator, we get:

edge = 2

So, the length of the edge of the compass cube is 2 inches.
### 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 8B:

Reasoning: Since the plot is a cube, all sides have the same length. The volume of a cube is calculated by multiplying the length of each side cubed (length × width × height = volume). In this case, the volume is 729 cubic meters, so we can set up the equation:

side × side × side = 729

To find the length of each side, we can take the cube root of 729:

side = ∛729

Using a calculator, we get:

side ≈ 9

So, the length of each side of the plot is approximately 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 8B:

Reasoning: Since the slide is a cuboid with the same length, width, and height, the volume can be represented as:

Volume = Length × Width × Height

Given that the volume is 1000 cubic feet, we can set up an equation:

Length × Width × Height = 1000

Since the length, width, and height are equal, we can let x be the length (and also the width and height). Then, the equation becomes:

x × x × x = 1000

Simplifying the equation, we get:

x³ = 1000

Taking the cube root of both sides:

x = ∛1000

x ≈ 10

So, the length of one side of the slide is approximately 10 feet.

### 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 8B:

Reasoning: Since the volume of the cube is 512 cubic feet, we can find the length of each side by taking the cube root of the volume.

Volume = side × side × side = 512 cubic feet

side × side × side = 512

side × side = 512 / side

side = √(512 / side)

side = √(2^9 / side)

side = 2^3 / side

side = 8 / side

side × side = 8

side = √8

side = 2√2

### Answer: 2√2 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?

Llama 3 8B:

Reasoning: Since the hat is a perfect cube, its volume is equal to the cube of its edge length. We can set up an equation using the volume and the edge length:

Volume = Edge^3
27 = Edge^3

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

Edge = ∛27

Using a calculator, we get:

Edge = 3

So, the length of one edge of the hat when it is fully inflated is 3 centimeters.

### 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 8B:

Reasoning: Let's call the number of grapes on each side of the cube "x". Since the container is a cube, all sides have the same number of grapes. The total number of grapes in the container is 27, which is the volume of the cube. The volume of a cube is calculated by multiplying the number of grapes on each side (x) cubed: x^3 = 27.

To find the value of x, we take the cube root of both sides: x = ∛27.

Using a calculator, we get: x ≈ 3.

So, each side of the cube holds approximately 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 8B:

Reasoning: Since the container is a cube, all its sides have the same length. The volume of a cube is calculated by multiplying the length of one side by itself twice (length × width × height = volume). In this case, the volume is given as 216 cubic meters, so we can set up the equation:

side × side × side = 216

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

side × side = ∛216

side = √(∛216)

side = √(6)

side = 2.4495 (approximately)

### Answer: 2.4495 (approximately)

Expected answer: 6

Correct? No

Problem: A cube-shaped bracelet charm has a volume of 64 mm^3. What is the length of each edge of the cube charm in millimeters?

Llama 3 8B:

Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each edge. We are given that the volume is 64 mm^3, so we can set up the equation:

64 = s^3

To solve for s, we can 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 8B:

Reasoning: Since the result of cubing a number is 64, we can find the number by taking the cube root of 64.
The cube root of 64 is 4, since 4^3 = 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 8B:

Since the mug is a cube, all its sides have the same length. The volume of the cube is given as 1 liter, which is the amount of hot drink it can hold.

The formula to find the volume of a cube is:

Volume = side × side × side

We know the volume is 1 liter, so we can set up the equation:

1 = side × side × side

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

side = ∛1

side = 1

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

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 8B:

Reasoning: The volume of a cube is equal to the length of one side cubed. So, if the volume is 343 cubic inches, we can set up the equation:

side^3 = 343

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

side = ∛343

side = 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 8B:

Reasoning: The volume of a cube is calculated by cubing the length of its side. Since the volume of the larger cube is 729 cubic cm, we can set up the equation:

side^3 = 729

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

side = ∛729

side = 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 8B:

Reasoning: Since the wheel is a cube, all its sides have the same length. Let's call this length "x". The volume of a cube is found by cubing its side length, so we can set up the equation:

x^3 = 216

To find the length of each side, we need to find the cube root of 216. This can be done using a calculator or by finding the perfect cube of a number that equals 216.

216 = 6^3

So, the length of each side of the wheel is 6 cm.

### 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 8B:

Reasoning: The volume of a cube is found by cubing the length of its edge. So, if the volume of the flower bud is 216 cubic millimeters, we can set up the equation:

edge^3 = 216

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

edge = ∛216

Using a calculator, we get:

edge = 6

So, each edge of the flower bud is 6 millimeters long.
### 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 8B:

Reasoning: The volume of a cube is found by cubing the length of one side. So, if the volume is 27 cm^3, we can set up the equation:

side^3 = 27

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

side = ∛27

side = 3

So, the length of each side of the snail's cubical shell is 3 centimeters.
### 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 8B:

Reasoning: The volume of a cube is equal to the length of one side cubed, or s^3. Since the volume of the party balloon is 27 cubic feet, we can set up the equation s^3 = 27.
Taking the cube root of both sides, we get s = ∛27.
Since ∛27 = 3, the length of one side of the balloon is 3 feet.
### 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 8B:

Reasoning: Since the tank is a cube, the volume of the tank can be found by cubing the length of one edge. The formula for the volume of a cube is V = s^3, where s is the length of one edge. We are given that the volume of the tank is 216 cubic feet, so we can set up the equation:

216 = s^3

To find the length of one edge, we need to find the cube root of 216. This can be done using a calculator or by finding the prime factorization of 216:

216 = 2^3 * 3^3

The cube root of 216 is the same as the product of the cube roots of 2^3 and 3^3:

s = √[2^3 * 3^3]
= √[8 * 27]
= √[216]
= 6

So, the length of one edge of the tank is 6 feet.

### 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 8B:

Reasoning: Since the box is a cube, all its sides have the same length. The volume of a cube is found by cubing its side length. So, the side length of the box is the cube root of the volume.

Let's call the side length "x". Then, we can set up the equation:

x^3 = 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: 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 8B:

Reasoning: Since the pocket is a cube, all its edges are equal. Let's call the length of each edge "x". The volume of a cube is calculated by multiplying the length of each edge cubed (x^3). We know the volume is 125 cubic inches, so 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 ≈ 4.64

Since the length of each edge cannot be a decimal, we round up to the nearest whole number to ensure the pocket is a perfect cube. Therefore, the length of each edge is:

x = 5 inches

### 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 8B:

Let's say the length of each side of the cube is x.

Since the cube is a 3D shape, the total number of flowers used is equal to the number of flowers on each side, which is x^3.

We know that the total number of flowers used is 125, so we can set up the equation:

x^3 = 125

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

x = ∛125

x = 5

So, the length of each side of the flower cube is 5.

### Answer: 5

Expected answer: 5

Correct? Yes

Problem: A farmer grows cucumbers in the shape of a perfect cube for a special contest. One of his cucumbers has a volume of 1000 cubic centimeters. What is the length in centimeters of a side of this cubic cucumber?

Llama 3 8B:

Reasoning: Since the cucumber is a perfect cube, its volume is equal to the length of its side cubed. We can set up an equation:

side^3 = 1000

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

side = ∛1000

side = 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 8B:

Reasoning: Since the volume of the cargo hold is 27 cubic meters, and all sides have equal length, we can use the formula for the volume of a cube (V = s^3) to solve for the length of one side.

Let's say the length of one side is s. Then, we can set up the equation:

27 = s^3

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

s = ∛27

s = 3

So, the length of one side of the cargo hold is 3 meters.

### 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 8B:

Reasoning: The volume of a cube is found by multiplying the length of each side by itself twice (length × width × height = volume). Since the volume of this cubic cucumber is 216 cubic centimeters, we can set up the equation:

side × side × side = 216

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

side = ∛216

Using a calculator, we find that:

side = 6

So, the length of each side of this 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 8B:

Reasoning: The volume of a cube is found by cubing the length of one edge. So, if the volume is 729 cubic feet, we can set up the equation:

length × length × length = 729

This is equivalent to:

length³ = 729

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

length = ∛729

Using a calculator, we get:

length = 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 8B:

Reasoning: The number 27 corresponds to the letter's position in the alphabet. We need to find the letter whose position is 27.
The alphabet starts from 'a' (position 1) to 'z' (position 26). To find the letter at position 27, we need to add 1 to 26, which gives us 27.
The letter at position 27 is 'aa' (since 'a' is the 1st letter and 'a' is the 26th letter). However, the problem statement says that the number corresponds to a number obtained by cubing a letter's position in the alphabet. This means we need to find the letter whose position is 3 (since 3^3 = 27).
The letter at position 3 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 8B:

Reasoning: Since the buoy is a cube, all its sides have the same length. Let's call this length "x". The volume of a cube is found by multiplying the length of each side cubed (x^3). Since the volume of the buoy is 1 cubic foot, we can set up the equation:

x^3 = 1

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

x = ∛1

x = 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 8B:

Let's denote the length of the object as L. Since the temperature at the heart of the object is directly proportional to the cube of its length, we can write:

Temperature ∝ L^3

We know that the temperature is 729 degrees, so we can set up the equation:

729 = kL^3

where k is the constant of proportionality.

To find the length L, we can divide both sides of the equation by k and take the cube root of both sides:

L = ∛(729/k)

Since we don't know the value of k, we cannot find the exact length of the object. However, we can express the length in terms of k.

### Answer: L = ∛(729/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?

Llama 3 8B:

Reasoning: The volume of a cube is found by cubing the length of its side. Since the volume of the cube-shaped orange is 8 cubic centimeters, we can set up the equation:

side^3 = 8

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

side = ∛8

side = 2

So, the length of each side of the cube-shaped orange is 2 centimeters.

### 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 8B:

Reasoning: The volume of a cubical box is given by the formula V = s^3, where s is the length of one edge of the box. In this case, the volume 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

Using a calculator, we find that:

s ≈ 9.0

So, the length of one edge of the box is approximately 9.0 centimeters.

### Answer: 9.0

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 8B:

Reasoning: Since the storage compartment is cubical, all its sides have the same length. Let's call this length "x". The volume of a cubical compartment is found by cubing its side length, so we can set up the equation:

x^3 = 125

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

x = ∛125

x = 5

So, the length of one side of the compartment is 5 inches.

### 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 8B:

Reasoning: Since the box is a cube, all its sides have the same length. The volume of a cube is found by cubing its side length. So, if the side length is x, then the volume is x^3.
We know the volume is 343 cubic inches, so we can set up the equation x^3 = 343.
Taking the cube root of both sides, we get x = ∛343.
Since 343 is a perfect cube (7^3), we can simplify this to x = 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 8B:

Reasoning: Since the package is a cube, the volume is equal to the edge length cubed (edge length)^3. We know the volume is 512 cubic centimeters, so 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

Using a calculator, we get:

edge length = 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 8B:

Reasoning: The volume of a cube is found by multiplying the length of a side by itself twice (length × width × height = volume). Since the volume is given as 512 cubic feet, we can set up the equation:

side × side × side = 512

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

side = ∛512

Using a calculator, we get:

side ≈ 8.0

So, the length of a side of this jungle gym is approximately 8.0 feet.

### Answer: 8.0

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 8B:

Reasoning: Since the toothbrush is a perfect cube, its volume is equal to the cube of its edge length. The volume of the toothbrush is given as 729 cubic centimeters, so we can set up the equation:

Edge length × Edge length × Edge length = 729

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

Edge length = ∛729

Using a calculator, we get:

Edge length = 9

So, the length of each edge of the toothbrush is 9 centimeters.
### 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 8B:

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

8 = s^3

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

s = ∛8

Using a calculator, we get:

s ≈ 2.08

So, the length of each edge of the star is approximately 2.08 light years.

### Answer: 2.08

Expected answer: 2

Correct? No

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 8B:

Reasoning: Let's say the length of each side of the cubical chamber is x. Since the chamber is filled with the dolphin's calls, the total volume of the calls is equal to the volume of the chamber, which is x^3.

We are given that the intensity of the call's volume is effectively 1 unit^3, which means that the total volume of the calls is 1 unit^3. Therefore, we can set up the equation:

x^3 = 1

Taking the cube root of both sides, we get:

x = ∛1

x = 1

So, the length of each side of the cubical chamber is 1 unit.
### 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 8B:

Reasoning: Since the gadget is a cube, all its sides have the same length. The volume of a cube is calculated by multiplying the length of each side cubed (length × width × height = volume). In this case, the volume is 1000 mm^3, so we can set up the equation:

side × side × side = 1000

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

side = ∛1000

side ≈ 10.0 mm

### Answer: 10.0 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 8B:

Reasoning: The volume of a cube is found by cubing the length of one edge. Since the volume of this cube is 1 cubic meter, we can set up the equation:

edge^3 = 1

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

edge = ∛1

Since ∛1 = 1, the length of one edge of this cube is 1 meter.

### 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 8B:

Reasoning: Since the box is a cube, all its sides have the same length. Let's call this length "x". The volume of a cube is found by multiplying the length of each side cubed (x^3). So, we can set up the equation:

x^3 = 216

To find the value of x, we need to find the cube root of 216. This can be done using a calculator or by finding the perfect cube of a number that equals 216. The perfect cube of 6 is 216, so:

x = √³216 = 6

So, each side of the magical cube-shaped box is 6 meters long.

### 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 8B:

Reasoning: The volume of a cube is found by cubing the length of one side. Since the volume of the house is 64 cubic feet, we can set up the equation:

side^3 = 64

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

side = ∛64

side = 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 8B:

Reasoning: The volume of a cubical object is found by cubing the length of its edge. So, if the volume is 1000 cubic centimeters, we can set up the equation:

edge^3 = 1000

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

edge = ∛1000

Using a calculator, we get:

edge = 10

So, the length of the edge of the toothbrush holder is 10 centimeters.

### 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 8B:

Reasoning: Since the oven is a cube, its volume is equal to the length of each side (f) cubed: 125 = f^3.
To find the length of each side, we take the cube root of both sides: f = ∛125.
Using a calculator, we get: f = 3.57 inches.
### Answer: 3.57

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?

Llama 3 8B:

Reasoning: The volume of a cube is found by multiplying the length of one side by itself three times (length × width × height = volume). Since the volume of the strawberry is 64 cubic millimeters, we can set up the equation:

side × side × side = 64

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

side = ∛64

side = 4

So, the length of one side of the strawberry is 4 millimeters.

### 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 8B:

Reasoning: Since the rocket is a perfect cube, its volume can be calculated by multiplying the length of each side cubed (side^3). The volume of the rocket is given as 216 cubic meters, so we can set up the equation:

side^3 = 216

To find the length of each side, we need to find the cube root of 216. This can be done using a calculator or by finding the prime factors of 216:

216 = 2^3 * 3^3

Taking the cube root of both sides:

side = ∛(2^3 * 3^3)
side = 2 * 3
side = 6

So, the length of each side of the rocket is 6 meters.

### 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 8B:

Reasoning: The volume of a cube is found by cubing the length of one edge. In this case, the volume is 512 cubic inches, so we can set up the equation:

edge^3 = 512

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

edge = ∛512

Using a calculator, we get:

edge = 8

So, the length of one edge of the base is 8 inches.

### Answer: 8

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 8B:

Reasoning: Since the eggs are arranged in a cubical arrangement, each side of the cube will have 27 eggs. To find the length of the edge of the cube, we can use the formula for the volume of a cube, which is side^3. Since the volume of the cube is equal to the number of eggs, we can set up the equation:

side^3 = 27

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

side = ∛27

side = 3

So, 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 8B:

Reasoning: Since the volume of a cube is given by the formula V = s^3, where s is the length of one edge, we can set up the equation 512 = s^3.
Taking the cube root of both sides, we get s = ∛512 = <<∛512=8>>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 8B:

Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each edge. We are given that the volume 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:

s = ∛343

Using a calculator, we get:

s ≈ 7

So, the length of each edge of the balloon is approximately 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 8B:

Reasoning: The volume of a cube is calculated by multiplying the length of one side by itself three times (length × width × height = volume). Since the volume of the shirt is 343 cubic centimeters, we can set up the equation:

side × side × side = 343

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

side = ∛343

Using a calculator or calculating the cube root by hand, we get:

side = 7

So, the length of one side of the cubic shirt design is 7 centimeters.

### 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 8B:

Reasoning: Since the roller skate is a cube, all its sides have the same length. Let's call this length "s". The volume of a cube is found by cubing its side length, so we can set up the equation:

s³ = 216

To find the value of s, we need to find the cube root of 216. This can be done using a calculator or by finding the perfect cube of a number that equals 216.

216 = 6³

So, 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 8B:

Reasoning: Since the tank is a cube, all its sides have the same length. Let's call this length "x". The volume of a cube is calculated by multiplying the length of each side cubed (x^3). In this case, the volume is given as 343 cubic meters.

So, we can set up the equation: x^3 = 343

To solve for x, we can take the cube root of both sides: x = ∛343

Using a calculator, we get: x ≈ 7

So, the side length of the cubic water tank is approximately 7 meters.

### 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 8B:

Reasoning: Since the backpack is cubical, all its sides have the same length. The volume of a cubical shape is found by cubing the length of one side. So, the length of one side is the cube root of the volume.

Let's find the length of one side:

√³216 = √(216^1/3) = √(6^3) = 6

So, the length of each side of the backpack is 6 inches.

### 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 8B:

Reasoning: Since the volume of the cube-shaped brain is 1 cubic meter, we can set up the equation:

side^3 = 1

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

side = ∛1

side = 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 8B:

Reasoning: Since the cluster of flowers is a perfect cube, its volume can be found by multiplying the length of its edge by itself three times. Let's call the length of the edge "x". Then, the volume of the cube is x^3.

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

x^3 = 1000

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

x = ∛1000

x = 10

So, the length of the edge of the flower cube is 10 centimeters.

### 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 8B:

Reasoning: Since the box is a cube, all its sides have the same length. Let's call this length "x". The volume of a cube is calculated by multiplying the length of each side cubed (x^3). In this case, the volume is 512 cubic inches, so we can set up the equation:

x^3 = 512

To find the length of one side, we need to find the cube root of 512. This can be done using a calculator or by finding the perfect cube of a number that equals 512. The perfect cube of 8 is 512 (8^3 = 8*8*8 = 512), so:

x = √[512] = √[8^3] = 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 8B:

Reasoning: The volume of a cube is found by cubing the length of one side. So, if the volume is 64 cubic inches, we can set up the equation:

side^3 = 64

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

side = ∛64

side = 4

So, the length of each side of the toy car is 4 inches.

### 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 8B:

Reasoning: Since the clock is a cube, all its sides have the same length. Let's call this length "x". The volume of a cube is found by cubing its side length, so we can set up the equation:

x^3 = 27

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

x = ∛27

x = 3

So, the length of each side of the clock is 3 inches.
### 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 8B:

Reasoning: Let's call the length of a side of the cubical cargo space "x". Since the volume of the cargo space is 8 cubic meters, we can set up the equation:

x × x × x = 8

Simplifying the equation, we get:

x³ = 8

Taking the cube root of both sides, we get:

x = ∛8

x ≈ 2.15

So, the length of a side of this cubical cargo space is approximately 2.15 meters.
### Answer: 2.15

Expected answer: 2

Correct? No

Problem: A grocer has a cubic box that perfectly fits 343 grapes in it. What is the length of the side of the box marked in grapes?

Llama 3 8B:

Reasoning: Since the box is cubic, all sides have the same length. Let's call this length "x". The volume of the box is given by the formula V = x^3, where V is the volume and x is the length of the side.

We know that the box can hold 343 grapes, so the volume of the box is equal to 343. We can set up the equation:

x^3 = 343

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

x = ∛343

x = 7

So, the length of the side of the box is 7 grapes.

### 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 8B:

Reasoning: Since the volume of the elephant is 343 cubic meters, and it has a perfect cube shape, we can find the length of each side by taking the cube root of the volume.

343 = a^3

Taking the cube root of both sides:

a = ∛343

a = 7

So, the length of each side of the cube is 7 meters.

### 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 8B:

Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge of the cube. Since the volume of each box is 27 cubic centimeters, we can set up the equation:

27 = s^3

To find the length of an edge of the box, we need to find the cube root of 27. This can be done using a calculator or by finding the perfect cube of 3, which is 27.

s = ∛27 = 3

So, the length of an edge of the box is 3 centimeters.

### 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 8B:

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

8 = s^3

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

s = ∛8

s = 2 km

### Answer: 2 km

Expected answer: 2

Correct? Yes

Problem: In a school, the students use cube-shaped backpacks to carry their books. One of these cube backpacks has a volume of 125 cubic inches. What is the length of each side of the backpack in inches?

Llama 3 8B:

Reasoning: The volume of a cube is found by cubing the length of one side. So, if the volume is 125 cubic inches, we can set up the equation:

side^3 = 125

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

side = ∛125

side = 5

So, the length of each side of the backpack is 5 inches.

### 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 8B:

Reasoning: The formula for the volume of a cube is V = s^3, where 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 = s^3

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

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 8B:

Reasoning: Since the treasure chest is a cube, its volume is equal to the length of each side cubed (V = s^3). We are given that the volume is 125 cubic feet, so we can set up the equation:

125 = s^3

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

s = ∛125

s = 5

So, the length of each side of the treasure chest is 5 feet.

### 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 8B:

Reasoning: Since the fish tank is a cube, all its sides have the same length. Let's call this length "x". The volume of a cube is calculated by multiplying the length of each side cubed, so we can set up the equation:

x^3 = 1 cubic meter

To find the length of each side, we need to find the cube root of 1 cubic meter. Since 1 cubic meter is equal to 1000 liters, we can convert it to meters:

1 cubic meter = 1000 liters = 1000/1000 = 1 meter

So, the length of each side is:

x = ∛1 = ∛(1 meter) = 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 8B:

Reasoning: Since the volume of a cube is equal to the length of one side squared, we can set up the equation:

125 = s^3

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

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

s = ∛125

s = 3.684

Since the length of one side cannot be a decimal, we round it to the nearest whole number:

s ≈ 4

### Answer: 4

Expected answer: 5

Correct? No

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 8B:

Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of the edge. We are given that the volume is 343, 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.
Using a calculator, we find that ∛343 ≈ 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 8B:

Reasoning: Since the box is cubical, all sides have the same length. Let's call this length "x". The volume of the box is the product of the length, width, and height, which is x^3. Since the volume is given as 1 cubic foot, we can set up the equation:

x^3 = 1

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

x = ∛1

x = 1

So, the length of a side of this box is 1 foot.

### 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 8B:

Reasoning: The volume of a cube is calculated by cubing the length of one side. In this case, the volume is 729 cubic units, so we can set up the equation:

side^3 = 729

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

side = ∛729

Using a calculator, we find that:

side = 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 8B:

Reasoning: Since the cookie dough is a cube, all its sides have the same length. Let's call this length "x". The volume of a cube is found by multiplying the length of each side cubed (x^3). So, we can set up the equation:

x^3 = 512

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

x = ∛512

x = 8

So, the length of each side of the cube is 8 cm.

### 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 8B:

Reasoning: The volume of a cubical hole is given by the formula V = s^3, where s is the length of the edge of the cube. In this case, the volume is 8 cubic feet, so we can set up the equation 8 = s^3.
To solve for s, we take the cube root of both sides: s = ∛8.
Using a calculator, we find that ∛8 ≈ 2.1.
### Answer: 2.1

Expected answer: 2

Correct? No

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 8B:

Reasoning: The problem states that the thickness of the string, in hundreds of a millimeter, cubed, will determine the pitch of a certain note. This means that the thickness of the string is cubed, so we can write an equation:

thickness³ = 343

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

thickness = ∛343

Using a calculator, we get:

thickness ≈ 6.48

So, the guitarist should choose a string with a thickness of approximately 6.48 hundreds of a millimeter.
### Answer: 6.48

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?

Llama 3 8B:

Reasoning: Since the compass box is a cube, all its edges have the same length. Let's call this length "x". The volume of a cube is found by cubing its edge length, so we can set up the equation:

x^3 = 729

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

x = ∛729

x = 9

So, the length of one edge of the cubical compass box is 9 cm.

### Answer: 9

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 8B:

Reasoning: The volume of a cube is given by the formula V = s^3, where s is the side length of the cube. We are given that the volume of one page is 64 cubic inches, so we can set up the equation:

64 = s^3

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

s = ∛64

s = 4

So, the side length of each page is 4 inches.
### Answer: 4

Expected answer: 4

Correct? Yes