### All GRE Math Resources

## Example Questions

### Example Question #21 : Solid Geometry

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:**

5*L*

2*L*^{3}

2*L*^{2}

8

4*L*^{3}

**Correct answer:**

2*L*^{3}

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* = 4*L*. Now we need volume = *L* * *W* * *H* = *L* * 4*L* * *L*/2 = 2*L*^{3}.

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

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

**Possible Answers:**

**Correct answer:**

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 #2 : 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:**

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 #3 : How To Find The Volume Of A Cube

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

**Possible Answers:**

**Correct answer:**

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 #4 : 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:**

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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