### All GRE Math Resources

## Example Questions

### Example Question #1 : Cubes

Quantity A: The length of a side of a cube with a volume of .

Quantity B: The length of a side of a cube with surface area of .

Which of the following is true?

**Possible Answers:**

Quantity B is larger.

The relationship between the two quantities cannot be determined.

Quantity A is larger.

The two quantities are equal

**Correct answer:**

The two quantities are equal

Recall that the equation for the volume of a cube is:

Since the sides of a cube are merely squares, the surface area equation is just times the area of one of those squares:

So, for our two quantities:

**Quantity A**

Use your calculator to estimate this value (since you will not have a square root key). This is .

**Quantity B**

First divide by :

Therefore,

Therefore, the two quantities are equal.

### Example Question #1 : Cubes

What is the length of an edge of a cube with a surface area of ?

**Possible Answers:**

**Correct answer:**

The surface area of a cube is made up of squares. Therefore, the equation is merely times the area of one of those squares. Since the sides of a square are equal, this is:

, where is the length of one side of the square.

For our data, we know:

This means that:

Now, while you will not have a calculator with a square root key, you do know that . (You can always use your calculator to test values like this.) Therefore, we know that . This is the length of one side

### Example Question #1 : Cubes

If a cube has a total surface area of square inches, what is the length of one edge?

**Possible Answers:**

There is not enough information given.

**Correct answer:**

There are 6 sides to a cube. If the total surface area is 54 square inches, then each face must have an area of 9 square inches.

Every face of a cube is a square, so if the area is 9 square inches, each edge must be 3 inches.