# GED Math : Volume of a Pyramid

## Example Questions

### Example Question #1 : Volume Of A Pyramid

The above square pyramid has volume 100. Evaluate  to the nearest tenth.

Explanation:

The volume of a square pyramid with base of area  and with height  is

.

The base, being a square of sidelength , has area . The height is . Therefore, setting , we solve for  in the equation

### Example Question #2 : Volume Of A Pyramid

A square pyramid whose base has sidelength  has volume . What is the ratio of the height of the pyramid to the sidelength of its base?

Explanation:

Since the correct answer is independent of the value of , for simplicity's sake, assume that .

The volume of a square pyramid with base of area  and with height  is

.

The base, being a square of sidelength 1, has area 1. In the volume formula, we set  and , and solve for :

This means that the height-to-sidelength ratio  is equal to , which is the correct response.

### Example Question #3 : Volume Of A Pyramid

Suppose a triangular pyramid has base area of 10, and a height of 6.  What is the volume?

Explanation:

Write the formula for the volume of a pyramid.

Substitute the known base area and the height into the formula.

### Example Question #4 : Volume Of A Pyramid

If the base of a pyramid is a square, with a length of 5, and the height of the pyramid is 9, what must be the volume?

Explanation:

Write the formula for the volume of pyramid.

The base area of a square is .

Substituting the side length:

Substitute the base area and the height.

### Example Question #1 : Volume Of A Pyramid

Suppose the base area of a pyramid is 24, and the height is 10.  What must the volume be?

Explanation:

Write formula for a pyramid.

Substitute the base and height.

### Example Question #6 : Volume Of A Pyramid

Find the volume of a pyramid with a square base area of  and a height of .

Explanation:

Write the formula of the volume of a pyramid.

The base area is represented by .  This means the volume is:

Substitute the base and height.

### Example Question #7 : Volume Of A Pyramid

Find the volume of a square pyramid with a base area of 12 and a height of 4.

Explanation:

Write the formula for the volume of a pyramid.

The base area constitutes  of the given equation.

Substitute values into the formula.

### Example Question #8 : Volume Of A Pyramid

Find the volume of a square pyramid if the base area is 2, and the height is 5.

Explanation:

Write the formula for the volume of a pyramid.

The base area constitutes , and can be replaced with the numerical area.

### Example Question #9 : Volume Of A Pyramid

If the length, width, and height of a pyramid is 2, 7, and 9, respectively, what must be the volume?

Explanation:

Write the formula for the volume of a pyramid.

### Example Question #10 : Volume Of A Pyramid

Find the volume of a pyramid with a length, width, and height of , respectively.