GRE Math : How to find the volume of a cube

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : How To Find The Volume Of A Cube

What is the volume of a rectangular box that is twice as long as it is high, and four times as wide as it is long?

Possible Answers:

4L3

2L3

5L

2L2

8

Correct answer:

2L3

Explanation:

The box is 2 times as long as it is high, so H = L/2. It is also 4 times as wide as it is long, so W = 4L. Now we need volume = L * W * H = L * 4L * L/2 = 2L3.

Example Question #2 : How To Find The Volume Of A Cube

What is the volume of a cube with a surface area of  ?

Possible Answers:

Correct answer:

Explanation:

The surface area of a cube is merely the sum of the surface areas of the  squares that make up its faces. Therefore, the surface area equation understandably is:

, where  is the side length of any one side of the cube. For our values, we know:

Solving for , we get:

 or 

Now, the volume of a cube is defined by the simple equation:

For , this is:

Example Question #3 : How To Find The Volume Of A Cube

The volume of a cube is . If the side length of this cube is tripled, what is the new volume?

Possible Answers:

Correct answer:

Explanation:

Recall that the volume of a cube is defined by the equation:

, where  is the side length of the cube. 

Therefore, if we know that , we can solve:

This means that .

Now, if we triple  to , the new volume of our cube will be:

Example Question #4 : How To Find The Volume Of A Cube

What is the volume of a cube with surface area of ?

Possible Answers:

Correct answer:

Explanation:

Recall that the equation for the surface area of a cube is merely derived from the fact that the cube's faces are made up of  squares. It is therefore:

For our values, this is:

Solving for , we get:

, so 

Now, the volume of a cube is merely:

Therefore, for , this value is:

Example Question #5 : How To Find The Volume Of A Cube

A cube has a volume of 64, what would it be if you doubled its side lengths?

Possible Answers:

Correct answer:

Explanation:

To find the volume of a cube, you multiple your side length 3 times (s*s*s).  

To find the side length from the volume, you find the cube root which gives you 4 

.  

Doubling the side gives you 8 

.  

The volume of the new cube would then be 512 

.

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