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?

DeepSeek 67B:

Reasoning:
The sandbox has the shape of a cubic box, which means all sides are equal in length.
The volume of a cube is calculated by multiplying the length of one side by itself twice (length x width x height).
In this case, the volume of the sandbox is given as 512 cubic feet.
Let's denote the length of each side as "s".
So, the volume of the sandbox is s x s x s = 512.
To find the length of each side, we need to solve the equation s^3 = 512.
Taking the cube root of both sides, we get s = ∛512.
Calculating the cube root of 512, we get s = 8.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula: V = s^3, where V is the volume and s is the length of each side.
We are given the volume of the fireplace, which is 729 cubic feet.
So, we can set up the equation: 729 = s^3.
To find the length of each side, we need to solve for s.
Taking the cube root of both sides of the equation, we get: s = ∛729.
Calculating the cube root of 729, we find that s = 9.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
In this case, the volume of the barn is 1000 cubic meters.
So, we can set up the equation 1000 = s^3 and solve for s.

Solution:
To solve for s, we take the cube root of both sides of the equation:
s = ∛1000
s = 10

Therefore, the length of each side of the barn is 10 meters.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of one side of the cube.
We are given that the volume of the tank is 512 m^3.
So, we can set up the equation 512 = a^3.
To find the length of one side of the tank, we need to solve for a.
We can take the cube root of both sides of the equation to get a = ∛512.
Calculating the cube root of 512 gives us a = 8.
Therefore, the size of one side of the tank is 8 meters.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cuboid is given by the formula: V = lwh, where l, w, and h are the length, width, and height of the cuboid, respectively.
Since all sides of the mountain are of equal length, we can denote the length of each side as x.
Therefore, the volume of the mountain can be expressed as V = x^3.
We are given that the volume of the mountain is 64 km^3, so we can set up the equation:
x^3 = 64
Solving for x:
x = ∛64
x = 4
The length of each side of the mountain 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of each edge.
We are given the volume of the crater, which is 512 cubic kilometers.
So, we can set up the equation 512 = a^3 and solve for a.

Solution:
To solve for a, we take the cube root of both sides of the equation:
a = ∛512
a = 8

Therefore, the length of each edge of the crater is 8 kilometers.
### 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?

DeepSeek 67B:

Reasoning:
The total number of blocks in a cube is equal to the length of one side cubed.
So, we need to find the cube root of the total number of blocks to find the length of one side.
The cube root of 343 is 7.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of one side.
We are given the volume V = 512 cubic feet.
To find the length of one side, we need to solve for s in the equation 512 = s^3.

Solution:
Taking the cube root of both sides of the equation, we get s = ∛512.
Calculating the cube root of 512, we find that s = 8.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of an edge.
We are given the volume of the eraser cube as 512 mm^3.
We can set up the equation 512 = a^3 and solve for a.

Solution:
512 = a^3
To solve for a, we take the cube root of both sides of the equation:
a = ∛512
a = 8
The edge length of each eraser cube is 8 mm.
### Answer: 8

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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by the formula: volume = side_length^3.
We are given that the volume of the cubic model is 8 cubic cm.
So, we can set up the equation: 8 = side_length^3.
To find the length of each side of the cube, we need to solve for side_length.

Solution:
We can solve for side_length by taking the cube root of both sides of the equation:
side_length = ∛8
side_length = 2 cm

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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by the formula: volume = edge_length^3.
We are given the volume of the cube as 27 cubic kilometers.
We can rearrange the formula to solve for the edge length: edge_length = cube_root(volume).

Solution:
edge_length = cube_root(27) = <<cube_root(27)=3>>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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself three times (length x width x height). In this case, the volume is given as 1 cubic inch.

Let's assume the length of each side of the box is x inches.

The volume of the box can be represented as x * x * x = 1 cubic inch.

To find the length of each side, we need to solve for x.

x^3 = 1

Taking the cube root of both sides:

x = ∛1

x = 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?

DeepSeek 67B:

Reasoning:
If each cubic centimeter of the flower holds 1 milliliter of nectar, then the total volume of the flower (in cubic centimeters) is equal to the total amount of nectar it holds (in milliliters).

Let's denote the length of one side of the flower as x. Since the flower is cubic, all sides have the same length. The volume of a cube is given by the formula:

Volume = side_length^3

In this case, the volume is equal to the amount of nectar the flower holds, which is 125 milliliters. Since 1 cubic centimeter is equal to 1 milliliter, we can convert the volume to cubic centimeters:

Volume = 125 cubic centimeters

Now we can set up the equation:

125 = x^3

To find the length of one side (x), we need to solve for x:

x^3 = 125

Taking the cube root of both sides:

x = ∛125

x = 5

So, the length of one side of the cubic flower is 5 centimeters.

Expected answer: 5

Correct? Yes

Problem: In a forest, the volume of a cubical tree stump was found to be 125 cubic meters. What is the length of one side of the tree stump?

DeepSeek 67B:

Reasoning:
The volume of a cuboid (which includes a cube) is given by the formula: Volume = length * width * height.
Since the tree stump is a cube, all its sides are equal in length.
Let's denote the length of one side as "s".
The volume of the tree stump is given as 125 cubic meters.
So, we can write the equation as: s * s * s = 125.

Solution:
We need to find the value of "s" (the length of one side of the tree stump).
s * s * s = 125
Taking the cube root of both sides, we get:
s = ∛125
s = 5

The length of one side of the tree stump is 5 meters.

Expected answer: 5

Correct? Yes

Problem: A jeweler is designing a bracelet in the shape of a cube. The volume of the bracelet is 1000 cubic millimeters. What is the length of each edge of the bracelet in millimeters?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of each edge.
We are given that the volume of the bracelet is 1000 cubic millimeters.
So, we can set up the equation 1000 = a^3.
To find the length of each edge, we need to solve for a.
Taking the cube root of both sides of the equation, we get a = ∛1000.
Calculating the cube root of 1000, we find that a = 10.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given that the volume of the soap is 1 cubic cm. So, we can set up the equation 1 = s^3.
To find the length of each side, we need to solve for s.

Solution:
Taking the cube root of both sides of the equation, we get s = ∛1 = 1.
Therefore, the length of each side of the soap is 1 cm.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of each edge.
We are given the volume of the yew tree as 216 cubic meters.
So, we can set up the equation 216 = a^3 and solve for a.

Solution:
216 = a^3
To solve for a, we take the cube root of both sides of the equation:
a = ∛216
a = 6

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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice (length x width x height). Since the blanket is folded into a perfect cube, all sides are equal in length. Let's denote the length of one side as x.

The volume of the cube is given as 1000 cubic cm. So, we can write the equation as:

x * x * x = 1000

Now, we need to solve for x.

x^3 = 1000

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

x = ∛1000

x = 10

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

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice (length x length x length).
In this case, the volume of the box is given as 125 cubic centimeters.
Let's denote the length of each side of the box as "s".
So, the equation for the volume of the box is s x s x s = 125.
To find the length of each side, we need to solve this equation for "s".

Solution:
We can rewrite the equation as s^3 = 125.
To solve for "s", we need to find the cube root of 125.
The cube root of 125 is 5.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice (length x length x length).
So, if the volume of the perfume bottle is 125 cubic centimeters, we can set up the equation:
side x side x side = 125
Let's solve for the length of one side:
side^3 = 125
To find the length of one side, we take the cube root of both sides of the equation:
side = ∛125
side = 5
The length of each side of the perfume 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of one side of the building as x. Since the building has a uniform cross-sectional area all along its height, the volume of the building can be represented as the product of the cross-sectional area and the height. Since the height, width, and depth are all equal, the cross-sectional area is x^2. The volume is given as 216 cubic meters, so we can write the equation:

x^2 * x = 216

Solving the equation:

x^3 = 216

To find the value of x, we need to find the cube root of 216:

x = ∛216
x = 6

So, the length in meters of one side of the building is 6 meters.

Expected answer: 6

Correct? Yes

Problem: A chair is designed in the shape of a cube, and its volume is 343 cubic feet. What is the length of each side of the chair in feet?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given that the volume of the chair is 343 cubic feet.
So, we can set up the equation 343 = s^3.
To find the length of each side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛343.
Calculating the cube root of 343, we find that s = 7.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice.
So, if the volume of each cube is 729 cubic inches, we can find the length of one side by taking the cube root of 729.
The cube root of 729 is 9.
Therefore, the length of one side of each cube is 9 inches.
The answer is: 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of each edge.
We are given that the volume of the spaceship is 8 cubic miles.
So, we can set up the equation 8 = a^3.
To find the length of each edge, we need to solve for a.
Taking the cube root of both sides of the equation, we get a = ∛8.
Calculating the cube root of 8, we find that a = 2.
Therefore, the length of each edge of the spaceship is 2 miles.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given the volume of the cold storage unit, which is 343 cubic feet.
So, we can set up the equation 343 = s^3 and solve for s.

Solution:
343 = s^3
To solve for s, we take the cube root of both sides of the equation:
s = ∛343
s = 7

The length of each side of the 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of the edge.
We are given that the volume of the compass cube is 8 cubic inches.
So, we can set up the equation 8 = s^3.
To find the length of the edge, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛8.
Calculating the cube root of 8, we find that s = 2.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice (length x length x length).
Since the volume of the plot is given as 729 cubic meters, we can set up the equation as follows:
length x length x length = 729
To find the length of each side, we need to find the cube root of 729.
The cube root of 729 is 9.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cuboid is given by the formula: volume = length * width * height.
Since the slide has the same length, width, and height, we can denote them all as x.
So, the volume of the slide is x * x * x = x^3.
We are given that the volume of the slide is 1000 cubic feet.
Therefore, x^3 = 1000.
To find the length of one side of the slide, we need to find the value of x.
We can solve for x by taking the cube root of both sides of the equation:
x = ∛1000.
Calculating the cube root of 1000, we get x = 10.
So, the length of one side of the slide is 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given that the volume of the play cube is 512 cubic feet.
So, we can set up the equation 512 = s^3.
To find the length of each side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛512.
Calculating the cube root of 512, we find that s = 8.
Therefore, the length of each side of the play cube is 8 feet.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a 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 27 = a^3.
To find the length of one edge, we need to solve for a.
We can take the cube root of both sides of the equation to get a = ∛27.
Calculating the cube root of 27 gives us a = 3.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The number of grapes in each container is equal to the volume of the cube. The volume of a cube is given by the formula:

Volume = side^3

We know that the volume of the cube is 27, so we can set up the equation:

27 = side^3

To find the length of each side, we need to solve for side:

side = ∛27

Calculating the cube root of 27, we get:

side = 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula: V = s^3, where V is the volume and s is the length of one side of the cube.
We are given the volume V = 216 cubic meters. We need to find the length of one side of the cube, which is s.

Solution:
We can rearrange the formula to solve for s: s = V^(1/3).
Substituting the given volume, we get: s = 216^(1/3).
Calculating this, we find that s = 6 meters.

Answer: The length of one side of the cube container is 6 meters.

Expected answer: 6

Correct? Yes

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

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of each edge.
We are given the volume of the cube charm, which is 64 mm^3.
We can set up the equation 64 = a^3 and solve for a.

Solution:
64 = a^3
To solve for a, we take the cube root of both sides of the equation:
a = ∛64
a = 4

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?

DeepSeek 67B:

Reasoning: If a number is cubed and the result is 64, then the number is the cube root of 64.
The cube root of 64 is 4.
### Answer: 4

Expected answer: 4

Correct? Yes

Problem: Your petite mug is perfect for hot chocolate and has a cubic shape, accommodating comfy 1 liter of hot drink. Can you tell me, how long, in liters, is each side of the petite mug?

DeepSeek 67B:

Reasoning:

The volume of a cube is given by the formula: V = a^3, where V is the volume and a is the length of each side.

In this case, the volume of the petite mug is 1 liter, so we can set up the equation:

1 = a^3

To find the length of each side, we need to solve for a.

Taking the cube root of both sides of the equation, we get:

a = ∛1

a = 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice (length x length x length).
So, if the volume of the cube-shaped blanket is 343 cubic inches, we can set up the equation:
length x length x length = 343
Let's solve for the length of one side of the fluffed blanket.

Solution:
We can rewrite the equation as:
length^3 = 343
To find the length, we need to take the cube root of both sides of the equation:
length = ∛343
length = 7
The length of one side of the fluffed blanket is 7 inches.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula: V = s^3, where s is the length of a side.
In this case, the volume of the larger cube is 729 cubic cm.
So, we can set up the equation: 729 = s^3, where s is the length of a side of the smaller cube.
To find the length of a side of the smaller cube, we need to find the cube root of 729.
The cube root of 729 is 9.
Therefore, the length of a side of the smaller 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given that the volume of the scooter wheel is 216 cubic cm.
So, we can set up the equation 216 = s^3.
To find the length of each side, we need to solve for s.
We can take the cube root of both sides of the equation to get s = ∛216.
Calculating the cube root of 216 gives us s = 6.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of each edge.
In this case, the volume of the flower bud is 216 cubic millimeters.
So, we can set up the equation 216 = a^3.
To find the length of each edge, we need to solve for a.
Taking the cube root of both sides of the equation, we get a = ∛216.
Calculating the cube root of 216, we find that a = 6.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given that the volume of the snail's shell is 27 cm^3.
So, we can set up the equation 27 = s^3 and solve for s.

Solution:
27 = s^3
To solve for s, we take the cube root of both sides of the equation:
s = ∛27
s = 3

The length of each side of the snail's cubical shell is 3 cm.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of one side.
We are given that the volume of the balloon is 27 cubic feet.
So, we can set up the equation 27 = s^3.
To find the length of one side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛27.
Calculating the cube root of 27, we find that s = 3.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of one edge.
We are given the volume of the tank, V = 216 cubic feet.
We need to find the length of one edge, a.
We can rearrange the formula to solve for a: a = V^(1/3).
Substituting the given volume, we get a = 216^(1/3).
Calculating this, we find a = 6 feet.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice (length x length x length).
So, if the volume of the box is 216 cubic inches, we can set up the equation:
length x length x length = 216
Let's solve for the length:
length^3 = 216
To find the length, we take the cube root of both sides of the equation:
length = ∛216
length = 6 inches
The length of one side of the box is 6 inches.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula: V = a^3, where V is the volume and a is the length of each edge.
We are given the volume of the pocket, which is 125 cubic inches.
So, we can set up the equation: 125 = a^3.
To find the length of each edge, we need to solve for a.
Taking the cube root of both sides of the equation, we get: a = ∛125.
Calculating the cube root of 125, we find that a = 5.
Therefore, the length of each edge of the pocket is 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?

DeepSeek 67B:

Reasoning:
The total number of flowers used is 125, and they are arranged in a cube shape.
A cube has 6 faces, and each face is a square.
Let's denote the length of each side of the cube as "s".
The total number of flowers used can be calculated as the product of the number of flowers on each face and the number of faces.
So, 125 = s^2 * 6.
Dividing both sides by 6, we get s^2 = 125/6.
Taking the square root of both sides, we get s = sqrt(125/6).
Calculating the square root, we get s = 5/sqrt(6).
So, the length of each side of the flower cube is 5/sqrt(6).
### Answer: 5/sqrt(6)

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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, 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 1000 = s^3.
To find the length of a side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛1000.
Calculating the cube root of 1000, we find that s = 10.
Therefore, the length of a side of the cubic cucumber is 10 centimeters.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of one side.
We are given that the volume of the cargo hold is 27 cubic meters.
So, we can set up the equation 27 = s^3.
To find the length of one side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛27.
Calculating the cube root of 27, we find that s = 3.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given the volume of the cubic cucumber as 216 cubic centimeters.
So, we can set up the equation 216 = s^3 and solve for s.

Solution:
216 = s^3
To find the length of each side, we need to find the cube root of 216.
The cube root of 216 is 6.
Therefore, 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)?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula: Volume = edge_length^3.
We are given the volume of the box, which is 729 cubic feet.
So, we can set up the equation: 729 = edge_length^3.
To find the length of one edge of the box, we need to solve for edge_length.
We can take the cube root of both sides of the equation to solve for edge_length: edge_length = ∛729.
Calculating the cube root of 729 gives us edge_length = 9.
Therefore, the length of one edge of the box is 9 feet.
### 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.)

DeepSeek 67B:

Reasoning:
We need to find a letter whose position when cubed equals 27.
Let's start by finding the cube root of 27:
The cube root of 27 is 3.
So, the letter we are looking for is the one that corresponds to the position 3 in the alphabet.
The answer 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
In this case, the volume of the buoy is 1 cubic foot.
So, we can set up the equation 1 = s^3.
To solve for s, we take the cube root of both sides of the equation:
s = ∛1 = 1
Therefore, 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the object as x. According to the problem, the temperature at the heart of the object is directly proportional to the cube of its length. Therefore, we can write the equation as:

T = k * x^3

where T is the temperature at the heart of the object, k is the constant of proportionality, and x is the length of the object.

We are given that the temperature at the heart of the object is 729 degrees. So, we can substitute the values in the equation:

729 = k * x^3

To find the length of the object, we need to determine the value of k. However, we don't have enough information to solve for k. Therefore, we cannot determine the length of the object in units.

### Answer: Cannot determine the length of the object in units.

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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by the formula: V = s^3, where V is the volume and s is the length of each side.
We are given the volume of the cube-shaped orange, which is 8 cubic centimeters.
So, we can set up the equation: 8 = s^3.
To find the length of each side, we need to solve for s.
We can take the cube root of both sides of the equation to isolate s: s = ∛8.
Calculating the cube root of 8 gives us s = 2.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of one edge.
In this case, the volume is 729 cubic centimeters.
So, we can set up the equation 729 = a^3.
To find the length of one edge, we need to solve for a.
Taking the cube root of both sides of the equation, we get a = ∛729.
Calculating the cube root of 729, we find that a = 9.
Therefore, the length of one edge of the box is 9 centimeters.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of one side.
We are given that the volume of the compartment is 125 cubic inches.
So, we can set up the equation 125 = s^3.
To find the length of one side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛125.
Calculating the cube root of 125, we find that s = 5.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given that the volume of the box is 343 cubic inches.
So, we can set up the equation 343 = s^3.
To find the length of each side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛343.
Calculating the cube root of 343, we find that s = 7.
Therefore, the length of each side of the box is 7 inches.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of an edge.
We are given that the volume of the candy package is 512 cubic centimeters.
So, we can set up the equation 512 = a^3.
To find the length of each edge, we need to solve for a.
Taking the cube root of both sides of the equation, we get a = ∛512.
Calculating the cube root of 512, we find that a = 8.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of a side.
We are given that the volume of the jungle gym is 512 cubic feet.
So, we can set up the equation 512 = s^3.
To find the length of a side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛512.
Calculating the cube root of 512, we find that s = 8.
Therefore, the length of a side of the jungle gym is 8 feet.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of each edge.
We are given the volume of the toothbrush, which is 729 cubic centimeters.
So, we can set up the equation 729 = a^3 and solve for a.

Solution:
729 = a^3
To find the length of each edge, we need to find the cube root of 729.
The cube root of 729 is 9.
Therefore, 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)?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where a is the length of each edge.
We are given that the volume of the star is 8 cubic light years.
So, we can set up the equation 8 = a^3.
To find the length of each edge, we need to solve for a.
Taking the cube root of both sides of the equation, we get a = ∛8.
Calculating the cube root of 8, we find that a = 2.
Therefore, the length of each edge of the star is 2 light years.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where s is the length of each side.
Since the intensity of the call's volume is effectively 1 unit^3, the volume of the chamber is 1 unit^3.
Therefore, we can set up the equation 1 = s^3.
Solving for s, we find that s = 1.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given the volume V = 1000 mm^3, so we can solve for the length of each side s.

Solution:
s^3 = 1000
s = ∛1000
s = 10

The length of each side of the cubic gadget is 10 millimeters.
### Answer: 10

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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one edge by itself twice (length x width x height). In this case, the volume is given as 1 cubic meter.

Let's denote the length of one edge as x.

The volume formula for a cube is:

Volume = x * x * x

We know that the volume is 1 cubic meter, so:

1 = x * x * x

To find the length of one edge (x), we need to solve for x:

x^3 = 1

Taking the cube root of both sides:

x = ∛1

x = 1

So, the length of one edge of the cube is 1 meter.

Expected answer: 1

Correct? Yes

Problem: A unicorn keeps her treasure in a magical cube-shaped box. The box has a volume of 216 cubic meters. How long is each side of this box in meters?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice. So, if we know the volume of the cube, we can find the length of one side by taking the cube root of the volume.

Solution:
The volume of the cube is 216 cubic meters. To find the length of one side, we take the cube root of 216.

The cube root of 216 is 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice (length x length x length).
Let's denote the length of one side of the house as "s".
We know that the volume of the house is 64 cubic feet, so we can write the equation as:
s x s x s = 64
Simplifying the equation, we get:
s^3 = 64
To find the length of one side, we need to find the cube root of 64.
The cube root of 64 is 4.
Therefore, the length of one side of the house is 4 feet.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cubical toothbrush holder is given by the formula V = a^3, where V is the volume and a is the length of the edge.
We are given that the volume of the toothbrush holder is 1000 cubic centimeters.
So, we can set up the equation 1000 = a^3.
To find the length of the edge, we need to solve for a.
Taking the cube root of both sides of the equation, we get a = ∛1000.
Calculating the cube root of 1000, we find that a = 10.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself three times (length * width * height). In this case, the volume of the cube-shaped oven is given as 125 cubic inches.

To find the length of each side of the loaf (f), we can use the formula for the volume of a cube:

Volume = f^3

We can set up the equation as follows:

125 = f^3

Now, we need to find the cube root of 125 to determine the length of each side of the loaf:

f = ∛125

f = 5

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

Expected answer: 5

Correct? Yes

Problem: A special variety of strawberry is shaped like a cube. The strawberry has a volume of 64 cubic millimeters. What is the length of one side of the strawberry in millimeters?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of one side.
We are given that the volume of the strawberry is 64 cubic millimeters.
So, we can set up the equation 64 = s^3.
To find the length of one side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛64.
Calculating the cube root of 64, we find that s = 4.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, 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 216 = s^3.
To find the length of each side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛216.
Calculating the cube root of 216, we find that s = 6.
Therefore, 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.

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of one edge.
We are given the volume of the lamp base, which is 512 cubic inches.
So, we can set up the equation 512 = a^3 and solve for a.

Solution:
512 = a^3
To solve for a, we take the cube root of both sides of the equation:
a = ∛512
a = 8

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?

DeepSeek 67B:

Reasoning:
The number of eggs laid by one fish is 27.
The eggs are arranged in a cubical pattern.
The number of eggs in each dimension of the cube is the cube root of the total number of eggs.
The cube root of 27 is 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'?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of one edge.
We are given the volume of the bus, V = 512 cubic meters.
We need to find the length of one edge, a.
We can rearrange the formula to solve for a: a = V^(1/3).
Substituting the given volume, we get a = 512^(1/3).
Calculating this, we find a = 8 meters.
Therefore, the length of one edge of the 'cube' is 8 meters.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of each edge.
We are given the volume of the balloon, which is 343 cubic meters.
We can set up the equation 343 = a^3 and solve for a.

Solution:
343 = a^3
To solve for a, we take the cube root of both sides of the equation:
a = ∛343
a ≈ 7.21 meters

The length of each edge of the balloon is approximately 7.21 meters.
### Answer: 7.21

Expected answer: 7

Correct? No

Problem: A shirt was created in a very unique 3D cube design with a total volume of 343 cubic centimeters. What is the length of one side of this cubic shirt design in centimeters?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice (length x length x length).
So, if we know the volume of the cube (343 cubic centimeters) and we want to find the length of one side, we can rearrange the formula to solve for the length.

Let's denote the length of one side as "s".

The formula for the volume of a cube is:

Volume = s x s x s

We can rearrange the formula to solve for "s":

s = (Volume)^(1/3)

Now, we can plug in the given volume (343 cubic centimeters) into the formula:

s = (343)^(1/3)

Calculating the cube root of 343:

s ≈ 7.31 centimeters

So, the length of one side of the cubic shirt design is approximately 7.31 centimeters.

Expected answer: 7

Correct? No

Problem: A roller skate is a cube-shaped container for a certain piece of equipment. It has a volume of 216 cubic inches. What is the length of each side of this roller skate container in inches?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given that the volume of the roller skate container is 216 cubic inches.
So, we can set up the equation 216 = s^3 and solve for s.

Solution:
216 = s^3
To solve for s, we take the cube root of both sides of the equation:
s = ∛216
s = 6

The length of each side of the roller skate container is 6 inches.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the side length.
We can rearrange this formula to solve for the side length: s = V^(1/3).

Plugging in the given volume of 343 cubic meters, we get:
s = 343^(1/3) = 7 meters.

So, the side length of the cubic water tank is 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given that the volume of the backpack is 216 cubic inches.
So, we can set up the equation 216 = s^3 and solve for s.

Solution:
216 = s^3
To solve for s, we take the cube root of both sides of the equation:
s = ∛216
s = 6

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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given that the volume of the dinosaur's brain is 1 cubic meter.
So, we can set up the equation 1 = s^3.
To find the length of each side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛1 = 1.
Therefore, the length of each side of the dinosaur's brain's cube structure is 1 meter.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of the edge.
In this case, the volume of the flower cluster is 1000 cubic centimeters.
So, we can set up the equation 1000 = a^3.
To find the length of the edge, we need to solve for a.
Taking the cube root of both sides of the equation, we get a = ∛1000.
Calculating the cube root of 1000, we find that a = 10.
Therefore, the edge of the flower cube is 10 centimeters long.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of one side.
In this case, the volume of the box is 512 cubic inches.
So, we can set up the equation 512 = s^3.
To find the length of one side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛512.
Calculating the cube root of 512, we find that s = 8.
Therefore, the length of one side of the box is 8 inches.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given that the volume of the toy car is 64 cubic inches.
So, we can set up the equation 64 = s^3.
To find the length of each side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛64.
Calculating the cube root of 64, we find that s = 4.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given that the volume of the cube-shaped clock is 27 cubic inches.
So, we can set up the equation 27 = s^3.
To find the length of each side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛27.
Calculating the cube root of 27, we find that s = 3.
Therefore, 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of a side of the cuboidal cargo space as x.
The volume of a cuboid is given by the formula: volume = length * width * height.
Since the height and width are the same length, we can write the formula as: volume = x * x * x.
We know that the volume is 8 cubic meters, so we can write the equation as: 8 = x * x * x.
To find the length of a side, we need to solve this equation for x.
We can rewrite the equation as: x^3 = 8.
Taking the cube root of both sides, we get: x = ∛8.
Calculating the cube root of 8, we get: x = 2.
Therefore, the length of a side of the cuboidal 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula: V = s^3, where V is the volume and s is the length of a side.
In this case, the volume of the box is 343 grapes, so we can set up the equation:
343 = s^3
To find the length of the side, we need to solve for s.
Taking the cube root of both sides of the equation, we get:
s = ∛343
s = 7
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given the volume of the elephant, which is 343 cubic meters.
So, we can set up the equation 343 = s^3.
To find the length of each side, we need to solve for s.
We can take the cube root of both sides of the equation to get s = ∛343.
Calculating the cube root of 343, we get s = 7.
Therefore, the length of each side of the elephant 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.

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of an edge.
In this case, the volume of the box is 27 cubic centimeters.
So, we can set up the equation 27 = a^3 and solve for a.

Solution:
27 = a^3
To solve for a, we take the cube root of both sides of the equation:
a = ∛27
a = 3

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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of an edge.
We are given the volume of the territory, which is 8 km^3.
So, we can set up the equation 8 = a^3 and solve for a.

Solution:
8 = a^3
To solve for a, we take the cube root of both sides of the equation:
a = ∛8
a = 2

The edge length of the territory is 2 kilometers.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given the volume of the backpack, which is 125 cubic inches.
So, we can set up the equation 125 = s^3 and solve for s.

Solution:
125 = s^3
To solve for s, we take the cube root of both sides of the equation:
s = ∛125
s = 5

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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice (length x width x height). Since all sides of a cube are equal, we can represent the length of one side as "s". Therefore, the volume of the cube can be represented as s x s x s, or s^3.

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

s^3 = 64

To find the length of each side, we need to solve for "s". Since we are dealing with a cube, the length of each side must be a positive number. We can start by taking the cube root of both sides of the equation:

s = ∛64

Taking the cube root of 64 gives us two possible values: 4 and -4. However, since the length of each side must be a positive number, we can disregard the negative value.

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

Expected answer: 4

Correct? Yes

Problem: A treasure chest has a cube shape. The volume of the treasure chest is 125 cubic feet. What is the length of each side of the treasure chest in feet?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given the volume of the treasure chest, which is 125 cubic feet.
So, we can set up the equation 125 = s^3.
To find the length of each side, we need to solve for s.
Taking the cube root of both sides of the equation, we get s = ∛125.
Calculating the cube root of 125, we find that s = 5.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We know that the volume of the fish tank is 1 cubic meter, so we can set up the equation 1 = s^3.
To solve for s, we take the cube root of both sides of the equation: s = ∛1 = 1.
Therefore, 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice (length x length x length). In this case, the volume of the cheese cube is given as 125 cubic centimeters.

Let's denote the length of one side of the cube as x.

The volume formula for a cube is:

Volume = x^3

We can set up the equation as follows:

125 = x^3

To find the length of one side (x), we need to solve for x by taking the cube root of both sides of the equation:

x = ∛125

Calculating the cube root of 125:

x = 5

So, the length of one side of the cheese cube is 5 centimeters.

Expected answer: 5

Correct? Yes

Problem: A roller skater is skating in a skatepark modeled as a perfect cube. The volume of the skatepark, in cubic meters, is 343. What is the length of the edges of the skatepark in meters?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of the edges.
We are given the volume of the skatepark, which is 343 cubic meters.
So, we can set up the equation 343 = a^3.
To find the length of the edges, we need to solve for a.
Taking the cube root of both sides of the equation, we get a = ∛343.
Calculating the cube root of 343, we find that a = 7.
Therefore, the length of the edges of the skatepark is 7 meters.
### 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of a side.
In this case, the volume of the box is 1 cubic foot.
So, we can set up the equation 1 = s^3.
To solve for s, we take the cube root of both sides of the equation:
s = ∛1 = 1
Therefore, the length of a side of the 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is calculated by multiplying the length of one side by itself twice (length x length x length).
In this case, the volume of the item cube is 729 cubic units.
To find the length of each side, we need to find the cube root of 729.
The cube root of 729 is 9.
Therefore, the length of each side of the item cube is 9 units.
The answer is: 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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
We are given the volume of the cube, which is 512 cubic cm.
So, we can set up the equation 512 = s^3 and solve for s.

Solution:
512 = s^3
To solve for s, we take the cube root of both sides of the equation:
s = ∛512
s = 8

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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula V = a^3, where V is the volume and a is the length of an edge.
In this case, the volume of the cubical hole is 8 cubic feet.
So, we can set up the equation 8 = a^3.
To find the length of the edge, we need to solve for a.
We can do this by taking the cube root of both sides of the equation.
a = ∛8 = 2 feet.
The length of the edge of the cubic hole is 2 feet.
### 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?

DeepSeek 67B:

Reasoning:
The formula for the pitch of a note is:
pitch = (thickness^3) / (length * tension)

We are given the pitch (343 Hz) and need to find the thickness of the string. We can rearrange the formula to solve for thickness:

thickness = (pitch * length * tension)^(1/3)

We don't have the values for length and tension, but we can assume that the guitarist has already set these values to achieve the desired pitch. Let's assume the length and tension are constants, L and T, respectively.

thickness = (343 * L * T)^(1/3)

Since the thickness is given in hundreds of a millimeter, we need to convert the result to this unit.

thickness = (343 * L * T)^(1/3) * 0.01

Now, we can plug in the values for pitch, length, and tension to find the thickness of the string.

thickness = (343 * L * T)^(1/3) * 0.01

The thickness of the string will be in hundreds of a millimeter.

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?

DeepSeek 67B:

Reasoning:
The volume of a cube is given by the formula: V = a^3, where V is the volume and a is the length of one edge.
We are given the volume of the cube, which is 729 cubic cm.
So, we can set up the equation: 729 = a^3.
To find the length of one edge, we need to solve for a.
We can take the cube root of both sides of the equation to solve for a: a = ∛729.
Calculating the cube root of 729 gives us a = 9.
Therefore, 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?

DeepSeek 67B:

Reasoning: The volume of a cube is given by the formula V = s^3, where V is the volume and s is the side length.
We can rearrange the formula to solve for s: s = V^(1/3).
In this case, the volume of one page is 64 cubic inches, so the side length of each page is 64^(1/3).
### Answer: 64^(1/3)

Expected answer: 4

Correct? No