### All SAT Math Resources

## Example Questions

### Example Question #1 : How To Find The Length Of An Edge Of A Cube

The number of square units in the surface area of a cube is twice as large as the number of cubic units in its volume. What is the cube's volume, in cubic units?

**Possible Answers:**

27

108

36

216

9

**Correct answer:**

27

The number of square units in the surface area of a cube is given by the formula 6s^{2}, where s is the length of the side of the cube in units. Moreover, the number of cubic units in a cube's volume is equal to s^{3}.

Since the number of square units in the surface area is twice as large as the cubic units of the volume, we can write the following equation to solve for s:

6s^{2} = 2s^{3}

Subtract 6s^{2} from both sides.

2s^{3} – 6s^{2} = 0

Factor out 2s^{2} from both terms.

2s^{2}(s – 3) = 0

We must set each factor equal to zero.

2s^{2} = 0, only if s = 0; however, no cube has a side length of zero, so s can't be zero.

Set the other factor, s – 3, equal to zero.

s – 3 = 0

Add three to both sides.

s = 3

This means that the side length of the cube is 3 units. The volume, which we previously stated was equal to s^{3}, must then be 3^{3}, or 27 cubic units.

The answer is 27.

### Example Question #1 : Solid Geometry

You own a Rubik's cube with a volume of . What is the edge length of the cube?

**Possible Answers:**

No enough information to solve.

**Correct answer:**

You own a Rubik's cube with a volume of . What is the edge length of the cube?

To solve for edge length, think of the volume of a cube formula:

Now, we have the volume, so just rearrange it to solve for side length: