# GMAT Math : Calculating the volume of a cube

## Example Questions

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### Example Question #1 : Calculating The Volume Of A Cube

What is the volume of a cube with a side length of ?

Explanation:

### Example Question #2 : Calculating The Volume Of A Cube

The length, width, and height of a rectangular prism, in inches, are three different prime numbers. All three dimensions are between six feet and seven feet. What is the volume of the prism?

It is impossible to tell from the information given.

Explanation:

Six feet and seven feet are equal to, respectively, 72 inches and 84 inches. There are three different prime numbers between 72 and 84 - 73, 79, and 83 - so these are the three dimensions of the prism in inches. The volume of the prism is

cubic inches.

### Example Question #3 : Calculating The Volume Of A Cube

The length of a diagonal of one face of a cube is . Give the volume of the cube.

The correct answer is not among the other responses.

Explanation:

A diagonal of a square has length  times that of a side, so each side of each square face of the cube has length . Cube this to get the volume:

### Example Question #4 : Calculating The Volume Of A Cube

The length of a diagonal of a cube is . Give the volume of the cube.

Explanation:

Let  be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,

Cube the sidelength to get the volume:

### Example Question #5 : Calculating The Volume Of A Cube

A sphere with surface area  is inscribed inside a cube. Give the volume of the cube.

Explanation:

The sidelength of the cube is the diameter of the inscribed sphere, which is twice that sphere's radius. The sphere has surface area , so the radius is calculated as follows:

The diameter of the sphere - and the sidelength of the cube - is twice this, or .

Cube this sidelength to get the volume of the cube:

### Example Question #6 : Calculating The Volume Of A Cube

A cube is inscribed inside a sphere with volume . Give the volume of the cube.

The correct answer is not given among the other responses.

Explanation:

The diameter of the circle - twice its radius - coincides with the length of a diagonal of the inscribed cube. The sphere has volume , so the radius is calculated as follows:

The diameter of the sphere - and the length of a diagonal of the cube - is twice this, or 6.

Now, let  be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,

The volume of the cube is the cube of this, or

### Example Question #7 : Calculating The Volume Of A Cube

A sphere with volume  is inscribed inside a cube. Give the volume of the cube.

Explanation:

The sidelength of the cube is the diameter of the inscribed sphere, which is twice that sphere's radius. The sphere has volume , so the radius is calculated as follows:

The diameter of the sphere - and the sidelength of the cube - is twice this, or 6. Cube this sidelength to get the volume of the cube:

### Example Question #8 : Calculating The Volume Of A Cube

The distance from one vertex of a cube to its opposite vertex is twelve feet. Give the volume of the cube.

Explanation:

Since we are looking at yards, we will look at twelve feet as four yards.

Let  be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,

yards.

Cube this sidelength to get the volume:

cubic yards.

### Example Question #9 : Calculating The Volume Of A Cube

An aquarium is shaped like a perfect cube; the area of each glass face is  square meters. If it is filled to the recommended  capacity, then how much water will it contain?

Note:  cubic meter  liters.

The correct answer is not given among the other choices.

Explanation:

A perfect cube has square faces; if a face has area 6.25 square meters, then each side of each face measures the square root of this, or 2.5 meters. The volume of the tank is the cube of this, or

cubic meters.

Its capacity in liters is  liters.

80% of this is

liters.

### Example Question #10 : Calculating The Volume Of A Cube

Which choice comes closest to the volume of a cube with surface area  square centimeters?

Explanation:

The suface area of a cube is six times the square of the length of one side, so solve for  in the following:

This is the sidelength in centimeters; since we are looking at meters, divide this by 100 to convert to  meters.

Cube this to get volume

cubic meters.

Of the given choices, 3.5 cubic meters comes closest.

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