GRE Math : How to find the volume of a cube

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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:

2L³

4L³

2L²

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.

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Example Question #1 : Cubes

What is the volume of a cube with a surface area of 150 $\displaystyle 150$ in^2 $\displaystyle in^2$?

Possible Answers:

$5\:in^3$ $\displaystyle 5\:in^3$

$25\:in^3$ $\displaystyle 25\:in^3$

$325\:in^3$ $\displaystyle 325\:in^3$

$150\:in^3$ $\displaystyle 150\:in^3$

$125\:in^3$ $\displaystyle 125\:in^3$

Correct answer:

$125\:in^3$ $\displaystyle 125\:in^3$

Explanation:

The surface area of a cube is merely the sum of the surface areas of the $\displaystyle 6$ squares that make up its faces. Therefore, the surface area equation understandably is:

$\displaystyle SA = 6*s^2$, where $\displaystyle s$ is the side length of any one side of the cube. For our values, we know:

$\displaystyle 150=6s^2$

Solving for $\displaystyle s$, we get:

25=s^2 $\displaystyle 25=s^2$ or s=5 $\displaystyle s=5$

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

V=s^3 $\displaystyle V=s^3$

For s=5 $\displaystyle s=5$, this is:

$V=5^3=125\:in^3$ $\displaystyle V=5^3=125\:in^3$

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

The volume of a cube is $64\:in^3$ $\displaystyle 64\:in^3$. If the side length of this cube is tripled, what is the new volume?

Possible Answers:

$1024\:in^3$ $\displaystyle 1024\:in^3$

$924\:in^3$ $\displaystyle 924\:in^3$

$192\:in^3$ $\displaystyle 192\:in^3$

$768\:in^3$ $\displaystyle 768\:in^3$

$1728\:in^3$ $\displaystyle 1728\:in^3$

Correct answer:

$1728\:in^3$ $\displaystyle 1728\:in^3$

Explanation:

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

V=s^3 $\displaystyle V=s^3$, where $\displaystyle s$ is the side length of the cube.

Therefore, if we know that V=64 $\displaystyle V=64$, we can solve:

64=s^3 $\displaystyle 64=s^3$

This means that s=4 $\displaystyle s=4$.

Now, if we triple $\displaystyle s$ to $\displaystyle 12$, the new volume of our cube will be:

$V=12^3 = 1728\:in^3$ $\displaystyle V=12^3 = 1728\:in^3$

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Example Question #331 : Geometry

What is the volume of a cube with surface area of $384\:in^2$ $\displaystyle 384\:in^2$?

Possible Answers:

$256\:in^3$ $\displaystyle 256\:in^3$

$224\:in^3$ $\displaystyle 224\:in^3$

$64\:in^3$ $\displaystyle 64\:in^3$

$512\:in^3$ $\displaystyle 512\:in^3$

$984\:in^3$ $\displaystyle 984\:in^3$

Correct answer:

$512\:in^3$ $\displaystyle 512\:in^3$

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 $\displaystyle 6$ squares. It is therefore:

SA=6s^2 $\displaystyle SA=6s^2$

For our values, this is:

$\displaystyle 384=6s^2$

Solving for $\displaystyle s$, we get:

64=s^2 $\displaystyle 64=s^2$, so s=8 $\displaystyle s=8$

Now, the volume of a cube is merely:

V=s^3 $\displaystyle V=s^3$

Therefore, for s=8 $\displaystyle s=8$, this value is:

$V=8^3=512\:in^3$ $\displaystyle V=8^3=512\:in^3$

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Example Question #24 : Solid Geometry

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

Possible Answers:

128 $\displaystyle 128$

512 $\displaystyle 512$

256 $\displaystyle 256$

500 $\displaystyle 500$

$\displaystyle 64$

Correct answer:

512 $\displaystyle 512$

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

$(\sqrt[3]{64})$ $\displaystyle (\sqrt[3]{64})$.

Doubling the side gives you 8

(4*2=8) $\displaystyle (4*2=8)$.

The volume of the new cube would then be 512

$\displaystyle (8*8*8=512)$.

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GRE Math : How to find the volume of a cube

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

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

Example Question #1 : Cubes

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

Example Question #331 : Geometry

Example Question #24 : Solid Geometry

All GRE Math Resources

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