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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
In this case, a = 8 feet.
Therefore, the length of each side of the sandbox is 8 feet.

Expected answer: 8

Correct? Yes

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

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(729/1).
The length of each side of the fireplace is approximately 27.48 feet.

Expected answer: 9

Correct? No

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

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Substituting the values, we get a = <1000/a^3>.
Solving for a, we get a = 1000^(1/3) ≈ 14.14 m.
Therefore, the length of each side of the barn is approximately 14.14 m.

Expected answer: 10

Correct? No

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
If the volume of the tank is 512 m^3, then the side length of the tank is sqrt(512) = <<sqrt(512)=19.8m>>19.8m.
### Answer: 19.8m

Expected answer: 8

Correct? No

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

Gemma 2B:

Reasoning: The volume of a cuboid is given by the formula V = a^3, where a is the length of each side.
Substituting the values, we get 64 = a^3.
Taking the cube root of both sides, we get a = <<∛64=4>>4 km.
Therefore, the length of each side of the mountain is 4 km.

Expected answer: 4

Correct? Yes

Problem: There's a large crater on the moon that has a cubic shape and a volume of 512 cubic kilometers. What is the length of each edge of this crater in kilometers?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Solving for a, we get a = sqrt(V/a) = sqrt(512/1).
Therefore, the length of each edge of the crater is sqrt(512) = 18.8 km.

Expected answer: 8

Correct? No

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?

Gemma 2B:

Reasoning: The number of blocks is divisible by 7, which is the number of sides of a cube. Therefore, the side length is 49 blocks.
### Answer: 49

Expected answer: 7

Correct? No

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

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(512/1).
The length of one side of the container is approximately 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?

Gemma 2B:

Reasoning: The edge length of each cube can be found by taking the cube root of 512.
Edge length = <sqrt512> mm = 24 mm.
### Answer: 24

Expected answer: 8

Correct? No

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
If V = 8 cm^3, then a = sqrt(V/a) = sqrt(8 cm^3) = 2 cm.
Therefore, the length of each side of the cube is 2 cm.

Expected answer: 2

Correct? Yes

Problem: A shark's territory within the ocean is allotted in the shape of a cube with a volume of 27 cubic kilometers. Can you calculate the length in kilometers of one edge of this cube?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Solving for a, we get a = (V)^(1/3).
Substituting the values, we get a = (27)^(1/3) = 3 km.
### 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(1 in^3) = 1 in.
The length of each side of the box is 1 inch.

Expected answer: 1

Correct? Yes

Problem: A unique type of flower grows in the shape of a cube. Each cubic centimeter of this flower holds 1 milliliter of nectar. If a particular flower holds 125 milliliters of nectar, what is the length of one side of this cubic flower in centimeters?

Gemma 2B:

Reasoning: The volume of the flower is equal to the side length of the cube.
Therefore, the side length of the flower is sqrt(125) cm = <<sqrt(125)=5cm>>5 cm.
### 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?

Gemma 2B:

Reasoning: The volume of a cubical tree stump is given by the formula V = a^3, where a is the length of one side of the stump.
Substituting the value of V = 125 into the formula, we get a = <125 ÷ 3>.
Therefore, the length of one side of the tree stump is 5 meters.

Expected answer: 5

Correct? Yes

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

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Solving for a, we get a = sqrt(V/a) = sqrt(1000/6).
The length of each edge of the bracelet is approximately 15.8 millimeters.
### Answer: 15.8

Expected answer: 10

Correct? No

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Substituting the value of V = 1 cm^3 into the formula, we get a = <1 cm^3)^(1/3} = 1 cm.
Therefore, the length of each side of the soap is 1 cm.

Expected answer: 1

Correct? Yes

Problem: A forest ranger discovered a rare cubic yew tree with a volume of 216 cubic meters. What is the length of each edge of this yew tree in meters?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Therefore, a = <V^(1/3)> = <216^(1/3)> = 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(1000 cm^3/1 cm^3) = 10 cm.
### Answer: 10 cm

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?

Gemma 2B:

Reasoning: The volume of the box is equal to the volume of the toy train, which is 125 cubic centimeters.
The volume of a cube is equal to the side length squared, so the side length of the box is sqrt(125) = 5 cm.
### Answer: 5 cm

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(125 cm^3/1 cm^3) = 5 cm.
The length of each side of the bottle is 5 cm.

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?

Gemma 2B:

Reasoning: The volume of a cuboid is given by the formula V = length * width * height.
We are given that V = 216 m^3.
We are also given that the width and height are equal.
Therefore, we can write the equation 216 = length * width * height.
Solving for the length, we get length = 216 / width * height.
Substituting the values of V, width and height, we get length = 216 / width * width = 216.
### Answer: 6 m

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(343/1).
The length of each side of the chair is approximately 11.5 inches.
### Answer: 11.5

Expected answer: 7

Correct? No

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

Gemma 2B:

Reasoning: The volume of a cube is equal to the side length squared, so the side length is sqrt(729) = <<sqrt(729)=27>>27 inches.

Expected answer: 9

Correct? No

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

Gemma 2B:

Reasoning: The length of each edge of the spaceship can be found by taking the square root of the volume.
Length = sqrt(8) = <<sqrt(8)=2√2>>2√2 miles.
### Answer: 2√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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Substituting the values, we get a = sqrt(343) = <<sqrt(343) ≈ 18.2 ft>>18.2 ft.
### Answer: 18.2

Expected answer: 7

Correct? No

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

Gemma 2B:

Reasoning: The edge of the cube is the square root of the volume.
Edge = sqrt(8) = <<sqrt(8)=2√2>>2√2 inches.
### Answer: 2√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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(729 m^3/1 m^3) = 27 m.
The length of each side of the plot is 27 m.

Expected answer: 9

Correct? No

Problem: A slide in the amusement park has a cuboid shape. The volume of this slide is given as 1000 cubic feet. If the slide has the same length, width, and height, what is the length of one side of the slide in feet?

Gemma 2B:

Reasoning: The volume of a cuboid is given by the formula V = length * width * height.
Given that the volume of the slide is 1000 cubic feet, and the volume is given by the formula V = length * width * height, we can write the equation 1000 = length * width * height.
Solving for the length, width, and height, we get the following equations:
length = width = height = 1000/30 = 33.33 feet.
### Answer: 33.33

Expected answer: 10

Correct? No

Problem: A zookeeper is building a new play cube for the monkeys. The volume of the cube is huge - exactly 512 cubic feet! The zookeeper wants all sides of the play cube to be of equal length. What is the length of each side of the play cube in feet?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(512/1).
Therefore, each side of the play cube is 8 feet long.
### 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
When the hat is fully inflated, its volume is 27 cm^3.
Therefore, a = sqrt(27 cm^3) = <<3 cm>>3 cm.
### Answer: 3 cm

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?

Gemma 2B:

Reasoning: Each side of the cube is the square root of 27, which is approximately <<3.66>>3.66.
Therefore, each side of the cube holds 3.66 grapes.
### Answer: 3.66

Expected answer: 3

Correct? No

Problem: A truck driver transports cargo in a big cube-shaped container. He knows that the volume of the container is given as 216 cubic meters. Can you help him find out the length of one side of the cube container?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Substituting the value of the volume into the formula, we get a = <V^(1/3)> = <216^(1/3)> = 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Solving for a, we get a = sqrt(V/a) = sqrt(64/1) = 4 mm.
The length of each edge of the cube charm is 4 mm.

Expected answer: 4

Correct? Yes

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

Gemma 2B:

Reasoning: 64 = 4^3.
The number is 4.

Expected answer: 4

Correct? Yes

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

Gemma 2B:

Reasoning: The volume of a cube is given by side^3.
Therefore, side = <math>\sqrt[3]{V}</math>, where V is the volume.
Given that the volume of the mug is 1 liter, we have side = <math>\sqrt[3]{1}</math> = 1 cm.
### Answer: 1 cm

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(343/1).
The length of one side of the blanket is approximately 11.5 inches.
### Answer: 11.5

Expected answer: 7

Correct? No

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

Gemma 2B:

Reasoning: The volume of the larger cube is 729 cm^3. The volume of each smaller cube is the cube root of 729 cm^3. Therefore, the side length of each smaller ice cube is the cube root of 729 cm^3.
### Answer: 15 cm

Expected answer: 9

Correct? No

Problem: A kid on a scooter notices that his new scooter wheel, which has a cubic shape, has a volume of 216 cubic cm. What is the length of each side of the wheel in cm?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
In this case, a = 6 cm.
Therefore, the length of each side of the wheel is 6 cm.

Expected answer: 6

Correct? Yes

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

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Therefore, a = (216)^(1/3} = 12 mm.
### Answer: 12

Expected answer: 6

Correct? No

Problem: A snail carries a shell that is shaped like a cube. The volume of the shell is 27 cm^3. What is the length of each side of the snail's cubical shell in centimeters?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
In this case, a = 3 cm.
Therefore, the length of each side of the snail's cubical shell is 3 cm.

Expected answer: 3

Correct? Yes

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

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
In this case, a = 3 feet.
Therefore, the length of one side of the balloon is 3 feet.

Expected answer: 3

Correct? Yes

Problem: A firefighter is pumping water out of a cubic tank to fight a fire. If the tank has a volume of 216 cubic feet, what is the length of one edge of the tank in feet?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Solving for a, we get a = <V^(1/3)> = <216^(1/3)> = 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for a, we get a = sqrt(V/a) = sqrt(216/1).
Therefore, the length of one side of the box is 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
The volume of the pocket is 125 = a^3.
Solving for a, we get a = sqrt(125/a).
Therefore, the edge length of each side of the pocket is 5 inches.

Expected answer: 5

Correct? Yes

Problem: A gardener arranged her flowers in a cube shape for an exhibition. The total number of flowers used was 125. What is the length of each side of the flower cube?

Gemma 2B:

Reasoning: The number of flowers in each layer of the cube is 5. The length of each side of the flower cube is the same as the length of one flower.
Therefore, the length of each side of the flower cube is 125 ÷ 5 = <<125 ÷ 5=25>>25 cm.

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Substituting the value of the volume, we get 1000 = a^3.
Taking the cube root of both sides, we get a = <<√1000≈31.6 cm>>31.6 cm.
### Answer: 31.6

Expected answer: 10

Correct? No

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length.
Therefore, a = (V)^(1/3) = (27)^(1/3) = 3 meters.
The length of one side of the cargo hold is 3 meters.

Expected answer: 3

Correct? Yes

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

Gemma 2B:

Reasoning: The volume of a cube is given by the formula side^3, where side is the length of each side.
In this case, side = sqrt(216) = <<sqrt(216)=14.4>>14.4 cm.
### Answer: 14.4

Expected answer: 6

Correct? No

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)?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of one edge.
Solving for a, we get a = sqrt(V/a) = sqrt(729/1).
Therefore, the length of one edge of the box is approximately 15.5 feet.

Expected answer: 9

Correct? No

Problem: The number 27 appears in a dream of a person who loves cryptic letters. He knows this number corresponds to a number obtained by cubing a letter's position in the alphabet. Can you find that letter by its position? (Let's use 'a' as 1, 'b' as 2, and so on.)

Gemma 2B:

The letter corresponding to the number 27 is '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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length.
Solving for the side length a, we get a = sqrt(V) = sqrt(1) = 1 foot.
### Answer: 1 foot

Expected answer: 1

Correct? Yes

Problem: The sun emits rays of energy that heat a cubical object to a temperature of 729 degrees. If the temperature at the heart of this object is directly proportional to the cube of its length, what is the length of the object in units?

Gemma 2B:

Reasoning: The temperature at the heart of the object is directly proportional to the cube of its length.
Therefore, the length of the object is inversely proportional to the cube of its length.
If the temperature at the heart of the object is 729 degrees, and the length is x units, then the length in units is inversely proportional to the cube of x, or x^−3.
Therefore, the length of the object is x = (1/729)^(1/3) = 10 cm.

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(8 cm^3/1 cm^3) = 2 cm.
Therefore, the length of each side of the cube-shaped orange is 2 centimeters.

Expected answer: 2

Correct? Yes

Problem: A particular telescope has a cubical mirror box where the volume of the box is 729 cubic centimeters. What is the length of one edge of this box, in centimeters?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of one edge.
Solving for a, we get a = sqrt(V/a) = sqrt(729 cm^3/1 cm^3) = 27 cm.
### Answer: 27

Expected answer: 9

Correct? No

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?

Gemma 2B:

Reasoning: The volume of a cuboid is given by the formula length x width x height. In this case, the length, width, and height are all equal to the side length of the compartment.
Therefore, the side length is 125 ÷ 3 = <<125 ÷ 3=41.67>>41.67 inches.

Expected answer: 5

Correct? No

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Substituting the value of the volume, 343 = a^3, we get a = <<∛343>> ≈ 18.5 inches.
### Answer: 18.5

Expected answer: 7

Correct? No

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

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Solving for a, we get a = <V^(1/3)> = <512^(1/3)> cm = 16 cm.
Each edge of a candy package is 16 cm.

Expected answer: 8

Correct? No

Problem: A solid cube jungle gym at the park has a volume of 512 cubic feet. What is the length of a side of this jungle gym in feet?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length.
Solving for a, we get a = sqrt(V/a) = sqrt(512/1).
The length of a side of the cube is approximately 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Solving for a, we get a = <V^(1/3)> = <729^(1/3)> cm.
The length of each edge of the toothbrush is approximately 15 cm.

Expected answer: 9

Correct? No

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

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
In this case, a = 8 light years.
Therefore, the length of each edge of the star is also 8 light years.
### Answer: 8

Expected answer: 2

Correct? No

Problem: A Dolphin can completely fill a cubical chamber with its calls, where the intensity of the call's volume is effectively 1 unit^3. What is the length of each side of the cubical chamber?

Gemma 2B:

Reasoning: The volume of the chamber is equal to the volume of the chamber filled with water, which is equal to the volume of the chamber filled with air.
Therefore, the side length of the chamber is equal to the square root of the volume of the chamber, which is equal to the volume of the chamber filled with air.
The volume of the chamber filled with air is equal to the volume of the chamber, which is equal to 1 unit^3.
Therefore, the side length of the chamber is equal to 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula a^3, where a is the side length.
Therefore, a = sqrt(1000) = <<sqrt(1000)=31.6 mm>>31.6 mm.
### Answer: 31.6

Expected answer: 10

Correct? No

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of one edge.
Solving for a, we get a = sqrt(V) = sqrt(1) = 1 meter.
### Answer: 1

Expected answer: 1

Correct? Yes

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

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length.
Solving for the side length, a = <V^(1/3)> = <216^(1/3)> = 6 meters.
### 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Substituting the values, we get a = <64/3> = 16 feet.
### Answer: 16

Expected answer: 4

Correct? No

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?

Gemma 2B:

Reasoning: The edge of the toothbrush holder is the square root of 1000 cubic centimeters.
The edge = sqrt(1000) cm = <<sqrt(1000) cm = 31.6 cm>>31.6 cm.
### Answer: 31.6

Expected answer: 10

Correct? No

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?

Gemma 2B:

Reasoning: The volume of the cube is equal to the side length squared, so we have the equation:

$$125 = f^3$$

$$f = \sqrt[3]{125}$$

$$f = 5$$

Therefore, the length of each side of the bread loaf 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for a, we get a = sqrt(V/a) = sqrt(64/1) = 4 cm.
The length of one side of the strawberry is 4 cm.

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(216/1).
The length of each side of the rocket is approximately 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.

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Solving for a, we get a = sqrt(V/a) = sqrt(512/1).
Therefore, the length of one edge of the base is 8 inches.

Expected answer: 8

Correct? Yes

Problem: A certain species of fish lays eggs in a cubical arrangement. If one fish lays 27 eggs, what is the length of the edge of this cube?

Gemma 2B:

Reasoning: The number of eggs laid by one fish is equal to the side length of the cube.
Therefore, the edge length of the cube = <math>\frac{27}{1}\end{math>cm = 27cm.
### Answer: 27

Expected answer: 3

Correct? No

Problem: The volume of a mini school bus is 512 cubic meters. If the shape of the bus can be closely approximated as a cube, then what is the length in meters of one edge of this 'cube'?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Therefore, a = sqrt(V/a) = sqrt(512/1) = 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Therefore, a = (V)^(1/3) = 343^(1/3) ≈ 18.5 meters.
### Answer: 18.5

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(343 cm^3/1 cm^3) = 19 cm.
### Answer: 19 cm

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(216/1).
The length of each side of the roller skate container is approximately 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?

Gemma 2B:

Reasoning: The side length of the tank can be found using the formula: <<side length = √(volume)>>.
Substituting the volume of 343 into the formula, we get: <<side length = √(343)>>.
Therefore, the side length of the tank is approximately 18.5 meters.

Expected answer: 7

Correct? No

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

Gemma 2B:

Reasoning: The volume of a cuboid is given by the formula V = a^3, where a is the length of each side.
Substituting the values, we get a = <216 ÷ 3^3 = 8>.
Therefore, the length of each side of the backpack is 8 inches.

Expected answer: 6

Correct? No

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?

Gemma 2B:

Reasoning: The side length of the brain's cube is equal to the cube root of 1 cubic meter.
Therefore, the length of each side of the brain's cube is <<sqrt(1)=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?

Gemma 2B:

Reasoning: The edge of the flower cube can be found using the formula for the volume of a cube: V = a^3, where a is the edge length.
Substituting the value of the volume into the formula, we get a = <1000 cm^3>^(1/3) = 10 cm.
### Answer: 10 cm

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?

Gemma 2B:

Reasoning: The volume of the box is equal to 512 cubic inches. The side length of the box can be found by taking the square root of 512.
The length of one side of the box is approximately <<sqrt(512)=19.8 inches>>19.8.
### Answer: 19.8

Expected answer: 8

Correct? No

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

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Substituting the value of the volume into the formula, we get a = <64 ÷ 8>.
Therefore, the length of each side of the toy car is 8 inches.

Expected answer: 4

Correct? No

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for a, we get a = <V^(1/3)> = <27^(1/3)> = 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?

Gemma 2B:

Reasoning: The volume of a cuboid is given by the formula V = length * width * height.
We are given V = 8 m^3 and two of the dimensions are the same length. Let x be the length of the side.
Then the width is also x.
Substituting these values into the formula, we get:
8 = x * x = x^2
Therefore, x = 2 m.
The length of a side of the cubical cargo space is 2 m.

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?

Gemma 2B:

Reasoning: The length of the side of the box is the square root of 343.
The length of the side of the box is approximately <<sqrt(343)~~19.14>>19.14 centimeters.
### Answer: 19.14

Expected answer: 7

Correct? No

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

Gemma 2B:

Reasoning: The volume of a cube is given by the formula side^3, where side is the length of each side.
If the volume of the elephant is 343 cubic meters, we can write the equation 343 = side^3.
Solving for side, we get side = sqrt(343) ≈ 18.5 meters.
### Answer: 18.5

Expected answer: 7

Correct? No

Problem: A camera company produces boxes for their cameras that are in the shape of a cube. The volume of each box is 27 cubic centimeters. Find the length of an edge of the box in centimeters.

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Solving for a, we get a = (V)^(1/3) = 27^(1/3) cm.
The length of an edge of the box is 3 cm.

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Solving for a, we get a = sqrt(V/a) = sqrt(8 km^3/a).
Therefore, a = 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = <V^(1/3)> = <125^(1/3)> = 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?

Gemma 2B:

Reasoning: The volume of the cube is given as 64 cubic meters.
The side length of the cube can be found using the formula: <<side length = √(volume)>>.
Substituting the value of the volume, we get: <<side length = √(64) = 8√2>>8√2 cubic meters.
### Answer: 8√2

Expected answer: 4

Correct? No

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Solving for the side length a, we get a = sqrt(V/a) = sqrt(125/a).
Therefore, the length of each side of the treasure chest is 5 feet.

Expected answer: 5

Correct? Yes

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

Gemma 2B:

Reasoning: The side length of the tank is sqrt(1) = 1 meter.
### Answer: 1 meter

Expected answer: 1

Correct? Yes

Problem: A chef is experimenting with cubed food presentations and crafts an appetizer from cheese. The appetizer's volume is 125 cubic centimeters. What is the length of one side of this cheese cube in centimeters?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula <math>V = a^3</math>, where a is the side length of the cube.
Substituting the values, we get <math>125 = a^3</math>.
Taking the cube root of both sides, we get <math>a = 5 cm</math>.
### Answer: 5 cm

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the edge length.
Solving for a, we get a = <V^(1/3)> = <343^(1/3)> cm.
The length of the edges of the skatepark is approximately 11.5 cm.

Expected answer: 7

Correct? No

Problem: An ice skate manufacturer has a design for cubical boxes to package a pair of skates. If the volume of this box is 1 cubic foot, what is the length of a side of this box in feet?

Gemma 2B:

Reasoning: The volume of a box is given by the formula V = a^3, where a is the side length of the box.
Solving for a, we get a = <V^(1/3)> = <1^3> = 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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length.
Solving for a, we get a = <V^(1/3)> = <729^(1/3)> = 27.
Therefore, the length of each side of the item cube is 27 units.

Expected answer: 9

Correct? No

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the side length of the cube.
Substituting the values, we get a = <512 cm / 8>.
Therefore, the length of each side of the cube is 64 cm.

Expected answer: 8

Correct? No

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?

Gemma 2B:

Reasoning: The volume of a cuboid is given by the formula V = a^3, where a is the length of the edge.
Substituting the values, we get V = 8 = a^3.
Therefore, a = 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?

Gemma 2B:

Reasoning: The pitch of a string is determined by its length and the tension of the string. The thickness of the string is not directly related to the pitch.
The pitch of 343 Hz is determined by the length of the string, which is determined by the gauge of the string.
The thickness of the string is not mentioned in the context, so we cannot determine the pitch of the string from the information provided.

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?

Gemma 2B:

Reasoning: The volume of a cube is given by the formula V = a^3, where a is the length of one edge of the cube.
Therefore, a = <V^(1/3)> = <729^(1/3)> cm.
### Answer: 15 cm

Expected answer: 9

Correct? No

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?

Gemma 2B:

Reasoning: The volume of a cube is given by side^3.
Therefore, side = <64 ÷ 3^3 = 4 inches.

Expected answer: 4

Correct? Yes