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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume V is 512 cubic feet, we can solve for s by taking the cube root of 512.
The cube root of 512 is 8, because 8 * 8 * 8 = 512.
### Answer: 8 feet

Expected answer: 8

Correct? Yes

Problem: An artisan carves a cubic fireplace out of stone, which has a volume of 729 cubic feet. What is the length of each side of the fireplace in feet?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. To find the length of a side, we need to find the cube root of the volume. The cube root of 729 is 9.
### Answer: 9

Expected answer: 9

Correct? Yes

Problem: A farmer has a large cubical barn with a volume of 1000 cubic meters. What is the length of each side of the barn in meters?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each side. To find the length of each side, we need to take the cube root of the volume.
The cube root of 1000 is 10, so 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?

Qwen2-Math 72B:

 Reasoning: Let the side of the tank be x. Then, x^3 = 512. Taking the cube root of both sides, we get x = 8.
### Answer: 8

Expected answer: 8

Correct? Yes

Problem: A mountain has a cuboidal shape and its volume is 64 km^3. If all of the sides of this cuboid are of equal length, what is the length of each side in kilometers?

Qwen2-Math 72B:

 Reasoning: Let the length of each side be x km. Then, the volume of the cuboid is x^3 = 64 km^3.
Therefore, x = 64^(1/3) = <<64^(1/3)=4>>4 km.
### 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of an edge. To find the length of an edge, we need to find the cube root of the volume. The cube root of 512 is 8.
### Answer: 8

Expected answer: 8

Correct? Yes

Problem: A baby is playing with blocks, assembling them to build a larger cube structure. If the total number of blocks is 343, what is the length (represented in blocks) of one side of the cube?

Qwen2-Math 72B:

 Reasoning: The total number of blocks is 343.
The length of one side of the cube is the cube root of 343, which is 7.
### Answer: 7

Expected answer: 7

Correct? Yes

Problem: An alien in a UFO spies a cubic container with a mysterious substance on earth. The volume of the substance is 512 cubic feet. The alien wonders, what is the length of one side of the cubic container in feet?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side of the cube.
We are given that the volume of the container is 512 cubic feet.
Therefore, we can set up the equation 512 = s^3.
To solve for s, we take the cube root of both sides of the equation:
s = cube root of 512
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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length of the cube.
Given that the volume of each cube is 512 mm^3, we can set up the equation 512 = a^3.
Taking the cube root of both sides, we get a = 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each side.
We are given that the volume V is 8 cubic cm.
So, we have 8 = s^3.
To find the length of each side, we need to find the cube root of 8.
The cube root of 8 is 2.
Therefore, 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of one edge.
Given that the volume V = 27 cubic kilometers, we can find the length of one edge by taking the cube root of the volume.
a = ∛V = ∛27 = <<27**(1/3)=3>>3 kilometers.
### Answer: 3 kilometers

Expected answer: 3

Correct? Yes

Problem: A deck of cards is designed in a cubic box. The volume of the box is 1 cubic inch. What is the length of each side of the box in inches?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each side. Since the volume of the box is 1 cubic inch, we have 1 = s^3. Taking the cube root of both sides, we get s = 1^(1/3) = 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?

Qwen2-Math 72B:

 Reasoning: Since the flower is in the shape of a cube, its volume can be calculated using the formula V = s^3, where s is the length of one side of the cube.
Given that the flower holds 125 milliliters of nectar, we can set up the equation 125 = s^3.
To find the length of one side, we need to find the cube root of 125.
The cube root of 125 is 5.
Therefore, the length of one side of the cubic flower is 5 centimeters.
### Answer: 5

Expected answer: 5

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: Let the length of one side of the tree stump be x meters.
Volume of the tree stump = x^3 cubic meters.
Given that the volume of the tree stump is 125 cubic meters, we have x^3 = 125.
Taking the cube root of both sides, we get x = 5.
### Answer: 5 meters

Expected answer: 5

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each edge. To find the length of each edge, we need to take the cube root of the volume. The cube root of 1000 is 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is calculated by cubing the length of one side. If the volume is 1 cubic cm, then the length of each side is the cube root of 1, which 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of an edge. To find the length of an edge, we need to find the cube root of the volume.
The cube root of 216 is 6.
### Answer: 6

Expected answer: 6

Correct? Yes

Problem: A blanket is folded in a perfect cube shape and has a volume of 1000 cubic cm. What is the length of each side of the blanket in centimeters?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is calculated by cubing the length of one side. Therefore, to find the length of one side, we need to take the cube root of the volume.
The cube root of 1000 is 10.
### Answer: 10

Expected answer: 10

Correct? Yes

Problem: A toy train is positioned inside a box, which is a cube. The volume of the box is 125 cubic centimeters. What is the length of each side of the box in centimeters?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume V is 125 cubic centimeters, we can find the length of a side by taking the cube root of the volume. The cube root of 125 is 5, because 5 * 5 * 5 = 125.
### Answer: 5 centimeters

Expected answer: 5

Correct? Yes

Problem: A perfume bottle is shaped like a cube and it has a volume of 125 cubic centimeters. What is the length of each side of the bottle in centimeters?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each side of the cube.
We are given that the volume of the perfume bottle is 125 cubic centimeters.
So, we can set up the equation: 125 = s^3
To solve for s, we need to take the cube root of both sides of the equation: s = cube root of 125
The cube root of 125 is 5, 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cuboid is given by the formula V = lwh, where l is the length, w is the width, and h is the height. Since the building is a pencil-shaped building with a uniform cross-sectional area all along its height, we can assume that the length, width, and height are all equal. Let's call this length/width/height "s". Then, the volume of the building is given by V = s^3. We are given that the volume of the building is 216 cubic meters. Therefore, we have s^3 = 216. Taking the cube root of both sides, we get s = 6. Therefore, the length of one side of the building 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume V is 343 cubic feet, we can find the length of a side by taking the cube root of the volume. The cube root of 343 is 7, because 7 * 7 * 7 = 343.
### Answer: 7 feet

Expected answer: 7

Correct? Yes

Problem: A roller skate company designs a new line of cubes that will go on the end of each skate. The volume of each cube is calculated to be 729 cubic inches. What is the length, in inches, of a side of each cube?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is calculated by cubing the length of one side. Therefore, to find the length of one side, we need to find the cube root of the volume.
The cube root of 729 is 9.
### Answer: 9

Expected answer: 9

Correct? Yes

Problem: An alien species uses cubical spaceships for traveling. The volume of one of these spaceships is 8 cubic miles. What is the length in miles of each edge of the spaceship?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. We are given that the volume V is 8 cubic miles. Therefore, we have 8 = s^3. To find the length of each edge, we need to find the cube root of 8. The cube root of 8 is 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. To find the length of a side, we need to find the cube root of the volume. The cube root of 343 is 7.
### Answer: 7

Expected answer: 7

Correct? Yes

Problem: The volume of the compass cube is 8 cubic inches. What is the length of the edge of the compass cube in inches?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is calculated by cubing the length of one of its edges. Therefore, to find the length of the edge, we need to find the cube root of the volume.
The cube root of 8 is 2.
### Answer: 2 inches

Expected answer: 2

Correct? Yes

Problem: A potato farmer has a unique farm and prefers to grow his potatoes in cubic plots. One plot has a volume that measures 729 cubic meters. What is the length of each side of the plot in meters?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is calculated by cubing the length of one side. Therefore, to find the length of one side, we need to find the cube root of the volume.
The cube root of 729 is 9.
### 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?

Qwen2-Math 72B:

 Reasoning: Since the slide is a cuboid with equal length, width, and height, it is a cube. The volume of a cube is given by the formula V = s^3, where s is the length of one side. Given that the volume is 1000 cubic feet, we can find the length of one side by taking the cube root of the volume. Therefore, the length of one side of the slide is the cube root of 1000, which 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume V is 512 cubic feet, we can find the length of a side by taking the cube root of the volume. The cube root of 512 is 8, because 8 * 8 * 8 = 512.
### Answer: 8 feet

Expected answer: 8

Correct? Yes

Problem: A magical hat inflates into the shape of a perfect cube. When fully inflated, its volume measures 27 cubic centimeters. Can you figure out the length of one edge of the hat when it is fully inflated?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of one edge.
We know that the volume of the cube is 27 cubic centimeters, so we can set up the equation 27 = a^3.
Taking the cube root of both sides, we get a = 3.
### Answer: 3

Expected answer: 3

Correct? Yes

Problem: A grape farmer is packing his grapes into cube-shaped containers. If one such container holds 27 grapes, how many grapes does each side of the cube hold?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. If the cube holds 27 grapes, then the volume of the cube is 27 cubic units. Therefore, s^3 = 27. Taking the cube root of both sides, we get s = 3.
### 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side of the cube.
We are given that the volume of the container is 216 cubic meters.
So, we have 216 = s^3.
To find the length of one side of the cube, we need to find the cube root of 216.
The cube root of 216 is 6.
Therefore, the length of one side of the cube container is 6 meters.
### Answer: 6

Expected answer: 6

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each edge. To find the length of each edge, we need to find the cube root of the volume.
The cube root of 64 is 4, so the length of each edge of the cube charm is 4 mm.
### Answer: 4

Expected answer: 4

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: Let the number be x. Then, x^3 = 64.
Taking the cube root of both sides, we get x = 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume V is 1 liter, we can solve for s as follows:
1 = s^3
Taking the cube root of both sides, we get:
s = 1^(1/3) = 1 liter
### Answer: 1 liter

Expected answer: 1

Correct? Yes

Problem: The volume of a cube-shaped blanket is 343 cubic inches when fully fluffed. What is the length of one side of this fluffed blanket in inches?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. Given that the volume is 343 cubic inches, we can find the length of one side by taking the cube root of the volume.
s = ∛343 = <<∛343=7>>7 inches
### Answer: 7 inches

Expected answer: 7

Correct? Yes

Problem: A Penguin has stacked ice cubes in a specific way to form a larger perfect cube. The volume of the larger cube made up of smaller cubes is 729 cubic cm. If each side of the smaller ice cube is the same length in cm, what is that length?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Since the volume of the larger cube is 729 cubic cm, we can find the length of a side by taking the cube root of 729. The cube root of 729 is 9, so the length of a side of the larger cube is 9 cm. Since the larger cube is made up of smaller cubes, and each side of the smaller cube is the same length, the length of a side of the smaller cube is also 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume V is 216 cubic cm, we can find the length of a side by taking the cube root of the volume. The cube root of 216 is 6.
### Answer: 6 cm

Expected answer: 6

Correct? Yes

Problem: A butterfly places an egg in a cubic flower bud. The volume of the bud is 216 cubic millimeters. What length, in millimeters, is each edge of this flower bud?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge.
We can find the length of an edge by taking the cube root of the volume.
The cube root of 216 is 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume V is 27 cm^3, we can find the length of a side by taking the cube root of the volume. The cube root of 27 is 3, so the length of each side of the snail's cubical shell is 3 cm.
### Answer: 3 cm

Expected answer: 3

Correct? Yes

Problem: For a party, a giant cubic party balloon is being used. If the volume of the balloon is 27 cubic feet, what is the length of one side of the balloon in feet?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side of the cube. In this case, the volume of the balloon is 27 cubic feet, so we can set up the equation 27 = s^3. To solve for s, we can take the cube root of both sides of the equation: s = ∛27 = 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one edge. To find the length of one edge, we need to take the cube root of the volume. The cube root of 216 is 6.
### Answer: 6

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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. To find the length of one side, we need to find the cube root of the volume.
The cube root of 216 is 6.
### Answer: 6 inches

Expected answer: 6

Correct? Yes

Problem: A designer is making a cube-shaped pocket for a skirt. She needs 125 cubic inches of fabric to create this uniquely shaped pocket. What is the length in inches of each edge of the pocket?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each edge. We know that the volume V is 125 cubic inches. Therefore, we can set up the equation 125 = s^3. To find the length of each edge, we need to find the cube root of 125. The cube root of 125 is 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each side. Since the total number of flowers used is 125, we have V = 125. Therefore, s^3 = 125. Taking the cube root of both sides, we get s = 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume is 1000 cubic centimeters, we can find the length of a side by taking the cube root of the volume. The cube root of 1000 is 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. We can find the length of one side by taking the cube root of the volume.
The length of one side of the cargo hold is the cube root of 27, which is 3.
### Answer: 3

Expected answer: 3

Correct? Yes

Problem: A cucumber farmer is experimenting with a new variety of cucumbers that grow in a perfect cubic shape. One of these cubic cucumbers has a volume of 216 cubic centimeters. What is the length of each side of this cubic cucumber in centimeters?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume V is 216 cubic centimeters, we can find the length of a side by taking the cube root of the volume. The cube root of 216 is 6, because 6 * 6 * 6 = 216.
### Answer: 6 centimeters

Expected answer: 6

Correct? Yes

Problem: A skateboard company designs a cubic box to ship its skateboards. If the volume of the box is 729 cubic feet, what is the length of one edge of the box (in feet)?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one edge of the cube.
We are given that the volume of the box is 729 cubic feet, so we can set up the equation 729 = s^3.
To solve for s, we take the cube root of both sides of the equation: s = ∛729.
The cube root of 729 is 9, so 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.)

Qwen2-Math 72B:

 Reasoning: We need to find a number that, when cubed, equals 27. The cube root of 27 is 3. Therefore, the letter is the third letter in the alphabet, which 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each side. Since the volume is 1 cubic foot, we have 1 = s^3. Taking the cube root of both sides, we get s = 1^(1/3) = 1.
### 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?

Qwen2-Math 72B:

 Reasoning: Let the length of the object be x units. Then, the temperature at the heart of the object is proportional to x^3. We know that the temperature at the heart of the object is 729 degrees. Therefore, we can write the equation: x^3 = 729. Taking the cube root of both sides, we get: x = 9.
### Answer: 9

Expected answer: 9

Correct? Yes

Problem: An orange was shaped perfectly into a cube, with its volume being 8 cubic centimeters. What is the length of each side of the cube-shaped orange in centimeters?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is calculated by cubing the length of one side. Therefore, the length of each side of the cube-shaped orange is the cube root of 8 cubic centimeters, which 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one edge. Given that the volume is 729 cubic centimeters, we can find the length of one edge by taking the cube root of the volume.
s = ∛729 = <<∛729=9>>9 centimeters.
### Answer: 9 centimeters

Expected answer: 9

Correct? Yes

Problem: A backpack has a cubical storage compartment. The volume of this compartment is 125 cubic inches. What is the length of one side of the compartment in inches?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side of the cube.
We are given that the volume V is 125 cubic inches.
So, we have 125 = s^3.
To find the length of one side, we need to find the cube root of 125.
The cube root of 125 is 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. We are given that the volume V is 343 cubic inches. To find the length of a side, we need to find the cube root of the volume.
The cube root of 343 is 7, since 7^3 = 343.
Therefore, the length of each side of the box is 7 inches.
### Answer: 7 inches

Expected answer: 7

Correct? Yes

Problem: A certain type of candy comes in cube-shaped packages. When you measured the volume of one of these packages, it turned out to be 512 cubic centimeters. How long is each edge of a candy package?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of an edge. To find the length of an edge, we need to find the cube root of the volume.
The cube root of 512 is 8.
### 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side.
We are given that the volume V is 512 cubic feet.
So, we have 512 = s^3.
To find the length of a side, we need to find the cube root of 512.
The cube root of 512 is 8.
Therefore, the length of a side of the cube 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of an edge. To find the length of an edge, we need to find the cube root of the volume. The cube root of 729 is 9.
### Answer: 9

Expected answer: 9

Correct? Yes

Problem: There's a star in a distance galaxy shaped like a perfect cube. Its volume is 8 cubic light years. What is the length of each edge of the star (in light years)?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. Given that the volume is 8 cubic light years, we can find the length of an edge by taking the cube root of the volume. So, s = ∛8 = <<∛8=2>>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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each side. Since the volume is 1 unit^3, we have 1 = s^3. Taking the cube root of both sides, we get s = 1.
### Answer: 1

Expected answer: 1

Correct? Yes

Problem: The volume of a cubic gadget inside a watch mechanism is 1000 mm^3. What is the length of each side of this cubic gadget in millimeters?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each side. To find the length of each side, we need to find the cube root of the volume. The cube root of 1000 mm^3 is 10 mm.
### Answer: 10 mm

Expected answer: 10

Correct? Yes

Problem: There is a cube with a volume of 1 cubic meter. Can you find the length of one edge of this cube in meters?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of one edge.
To find the length of one edge, we need to find the cube root of the volume.
The cube root of 1 is 1.
### Answer: 1 meter

Expected answer: 1

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The volume of a cube is calculated by cubing the length of one side. If the volume is 216 cubic meters, then the length of one side is the cube root of 216.
The cube root of 216 is 6.
### Answer: 6 meters

Expected answer: 6

Correct? Yes

Problem: A cube-shaped house has a volume of 64 cubic feet. What is the length of one side of the house in feet?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. Given that the volume is 64 cubic feet, we can set up the equation 64 = s^3. To find the length of one side, we take the cube root of both sides of the equation, which gives us s = ∛64 = 4 feet.
### Answer: 4 feet

Expected answer: 4

Correct? Yes

Problem: The volume of a cubical toothbrush holder is 1000 cubic centimeters. What is the length in centimeters of the edge of the toothbrush holder?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of an edge. Therefore, a = V^(1/3) = 1000^(1/3) = <<1000^(1/3)=10>>10 cm.
### 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = f^3, where f is the length of each side of the cube.
Given that the volume of the oven is 125 cubic inches, we can set up the equation 125 = f^3.
To find the length of each side of the loaf, we need to find the cube root of 125.
The cube root of 125 is 5.
Therefore, the length of each side of the loaf is 5 inches.
### Answer: 5

Expected answer: 5

Correct? Yes

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

Qwen2-Math 72B:

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

Qwen2-Math 72B:

 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.
Given that the volume of the rocket is 216 cubic meters, we can set up the equation 216 = s^3.
To solve for s, we take the cube root of both sides of the equation: 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.

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one edge. To find the length of one edge, we need to find the cube root of the volume.
The cube root of 512 is 8.
### 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?

Qwen2-Math 72B:

 Reasoning: The number of eggs laid by one fish is 27, which is the volume of the cube.
The length of the edge of the cube is the cube root of the volume, which 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'?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of one edge.
To find the length of one edge, we can take the cube root of the volume: a = ∛V = ∛512 = <<∛512=8>>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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. To find the length of an edge, we need to find the cube root of the volume. The cube root of 343 is 7.
### 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side.
To find the length of one side, we need to find the cube root of the volume.
The cube root of 343 is 7.
Therefore, 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume is 216 cubic inches, we can find the length of a side by taking the cube root of the volume. The cube root of 216 is 6.
### Answer: 6 inches

Expected answer: 6

Correct? Yes

Problem: There's a cubic water tank which can hold up to 343 cubic meters of water. What is the side length of this cubic water tank?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is calculated by side length cubed. Therefore, the side length of the cubic water tank is the cube root of 343, which is 7.
### Answer: 7

Expected answer: 7

Correct? Yes

Problem: A backpack has a cubical shape and can hold a volume of 216 cubic inches. What is the length of each side of the backpack in inches?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. We are given that the volume V is 216 cubic inches. We can solve for s by taking the cube root of both sides of the equation: s = ∛V = ∛216 = 6 inches.
### Answer: 6 inches

Expected answer: 6

Correct? Yes

Problem: A scientist studying a particular type of dinosaur discovered that the volume of the dinosaur's cube-shaped brain was 1 cubic meter. What is the length in meters of each side of the dinosaur's brain's cube structure?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume V is 1 cubic meter, we can solve for s by taking the cube root of the volume: s = ∛V = ∛1 = 1 meter.
### Answer: 1 meter

Expected answer: 1

Correct? Yes

Problem: A certain species of flower grows in clusters shaped as perfect cubes. One cluster of flowers has a volume of 1000 cubic centimeters. How long, in centimeters, is the edge of this flower cube?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of the edge of the cube. In this case, we know that the volume of the cube is 1000 cubic centimeters, so we can set up the equation 1000 = s^3. To solve for s, we need to take the cube root of both sides of the equation. The cube root of 1000 is 10, so the length of the edge of the 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of one side. Given that the volume V is 512 cubic inches, we can find the length of one side by taking the cube root of the volume. Therefore, s = ∛512 = <<∛512=8>>8 inches.
### Answer: 8 inches

Expected answer: 8

Correct? Yes

Problem: A toy car toy is designed in the shape of a cube. If the toy car has a volume of 64 cubic inches, what is the length in inches of each side of the toy car?

Qwen2-Math 72B:

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

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. We are given that the volume V is 27 cubic inches. We can set up the equation 27 = s^3 and solve for s.
Taking the cube root of both sides, we get s = ∛27 = 3 inches.
### Answer: 3 inches

Expected answer: 3

Correct? Yes

Problem: A semi-truck has a cuboidal trailer. The volume of the cargo space in the trailer is 8 cubic meters, but the height and width are both the same length. What is the length of a side of this cubical cargo space?

Qwen2-Math 72B:

 Reasoning: The volume of a cuboid is given by the formula V = lwh, where l is the length, w is the width, and h is the height. Since the height and width are the same, we can say that w = h. Therefore, the volume of the cuboidal trailer can be written as V = l^2 * h. We are given that V = 8 cubic meters and w = h. Substituting these values into the formula, we get 8 = l^2 * h. Since w = h, we can substitute h for w in the equation, giving us 8 = l^2 * l. Simplifying this equation, we get 8 = l^3. Taking the cube root of both sides, we get l = 2. Therefore, the length of a side of this cubical cargo space is 2 meters.
### Answer: 2

Expected answer: 2

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The volume of the box is 343 cubic grapes.
The length of the side of the box is the cube root of the volume.
The cube root of 343 is 7.
### Answer: 7

Expected answer: 7

Correct? Yes

Problem: The volume of an elephant is approximately 343 cubic meters. If the elephant has a perfect cube shape, what is the length of each side in meters?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each side. To find the length of each side, we need to find the cube root of the volume.
The cube root of 343 is 7, so 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.

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of an edge. We are given that the volume is 27 cubic centimeters, so we can set up the equation 27 = s^3. Taking the cube root of both sides, we get s = 3. Therefore, 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
We can find the edge length by taking the cube root of the volume: a = ∛V = ∛8 = <<cbrt(8)=2>>2 km.
### Answer: 2 km

Expected answer: 2

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume is 125 cubic inches, we can set up the equation 125 = s^3. To find the length of each side, we take the cube root of 125, which is 5 inches.
### Answer: 5 inches

Expected answer: 5

Correct? Yes

Problem: A particular superhero has the ability to enclose villains in a cube of energy. If the cube has a volume of 64 cubic meters, what is the length of each side of the cube?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Given that the volume is 64 cubic meters, we can find the length of a side by taking the cube root of the volume. The cube root of 64 is 4.
### Answer: 4 meters

Expected answer: 4

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The volume of a cube is calculated by cubing the length of one side. Therefore, the length of one side of the treasure chest is the cube root of the volume.
The cube root of 125 is 5.
### Answer: 5

Expected answer: 5

Correct? Yes

Problem: A fish tank in the shape of a cube holds exactly 1 cubic meter of water. What is the length, in meters, of each side of the fish tank?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Since the volume of the fish tank is 1 cubic meter, we have 1 = s^3. Taking the cube root of both sides, we get s = 1^(1/3) = 1.
### 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is calculated by cubing the length of one side. Therefore, to find the length of one side, we take the cube root of the volume. The cube root of 125 is 5.
### Answer: 5

Expected answer: 5

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of the edges of the cube.
To find the length of the edges of the skatepark, we need to find the cube root of the volume.
The cube root of 343 is 7.
Therefore, the length of the edges of the skatepark is 7 meters.
### Answer: 7

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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of a side. Since the volume is 1 cubic foot, we have 1 = s^3. Taking the cube root of both sides, we get s = 1^(1/3) = 1.
### Answer: 1

Expected answer: 1

Correct? Yes

Problem: In a video game, a player notices that a treasure chest contains an item cube with a volume of 729 cubic units. What is the length of each side of the item cube?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each side. To find the length of each side, we need to find the cube root of the volume. The cube root of 729 is 9.
### 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?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the length of each side. To find the length of each side, we need to find the cube root of the volume.
The cube root of 512 is 8.
### Answer: 8

Expected answer: 8

Correct? Yes

Problem: A tree has a cubical hole in its trunk. The volume of the cubical hole is 8 cubic feet. What is the length of the edge of this cubic hole in feet?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of the edge of the cube.
Given that the volume of the cubical hole is 8 cubic feet, we can set up the equation 8 = a^3.
To find the length of the edge, we need to find the cube root of 8.
The cube root of 8 is 2.
Therefore, 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?

Qwen2-Math 72B:

 Reasoning: Let the thickness of the string be x. Then, x^3 = 343. Taking the cube root of both sides, we get x = 7.
### Answer: 7

Expected answer: 7

Correct? Yes

Problem: The cubic area of the compass box is 729 cubic cm. What is the length of one edge of this cubical compass box, given that it is a cube?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of one edge. Given that the volume is 729 cubic cm, we can find the length of one edge by taking the cube root of the volume.
The cube root of 729 is 9.
### Answer: 9 cm

Expected answer: 9

Correct? Yes

Problem: A book is written with a unique style where every page is in the shape of a cube. If the volume of one page is 64 cubic inches, what is the side length of each page?

Qwen2-Math 72B:

 Reasoning: The volume of a cube is given by the formula V = s^3, where s is the side length of the cube.
Given that the volume of one page is 64 cubic inches, we can set up the equation 64 = s^3.
Taking the cube root of both sides, we get s = 4 inches.
### Answer: 4 inches

Expected answer: 4

Correct? Yes