### All GED Math Resources

## Example Questions

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

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

**Possible Answers:**

**Correct answer:**

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 #1 : 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?

**Possible Answers:**

**Correct answer:**

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 #1 : Volume Of A Pyramid

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

**Possible Answers:**

**Correct answer:**

Write the formula for the volume of a pyramid.

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

The answer is:

### Example Question #1 : 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?

**Possible Answers:**

**Correct answer:**

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.

The answer is:

### 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?

**Possible Answers:**

**Correct answer:**

Write formula for a pyramid.

Substitute the base and height.

The answer is:

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

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

**Possible Answers:**

**Correct answer:**

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.

The answer is:

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

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

**Possible Answers:**

**Correct answer:**

Write the formula for the volume of a pyramid.

The base area constitutes of the given equation.

Substitute values into the formula.

The answer is:

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

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

**Possible Answers:**

**Correct answer:**

Write the formula for the volume of a pyramid.

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

The answer is:

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

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

**Possible Answers:**

**Correct answer:**

Write the formula for the volume of a pyramid.

The answer is:

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

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

**Possible Answers:**

**Correct answer:**

Write the volume formula for the pyramid.

Substitute the dimensions.

The answer is: