# Pre-Algebra : Volume of a Pyramid

## Example Questions

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

Principal O'Shaughnessy has a paperweight in the shape of a pyramid with a square base.  If one side of the base has a length of 4cm and the height of the paperweight is 6cm, what is the volume of the paperweight?

Explanation:

We begin by recalling the volume of a pyramid.

where  is the area of the base and  is the height.

Since the base is a square, we can find the area by squaring the length of one of the sides.

Given the height is 6cm, we can now calculate the volume.

Since all of the measurements were in centimeters, our volume will be in cubic centimeters.

Therefore, the volume of Principal O'Shaughnessy's paperweight is .

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

The volume of a square pyramid is . If a side of the square base measures . What is the height of the pyramid?

Explanation:

The formula for the volume of a pyramid is , where  is the area of the base and  is the height.

Using this formula,

= Area of the base, which is nothing but area of square with side

Now,  when simplified, you get .

Hence, the height of the pyramid is .

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

A pyramid has height 4 feet. Its base is a square with sidelength 3 feet. Give its volume in cubic inches.

Explanation:

Convert each measurement from inches to feet by multiplying it by 12:

Height: 4 feet =  inches

Sidelength of the base: 3 feet =  inches

The volume of a pyramid is

Since the base is a square, we can replace :

Substitute

The pyramid has volume 20,736 cubic inches.

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

The height of a right pyramid is  feet. Its base is a square with sidelength  feet. Give its volume in cubic inches.

Explanation:

Convert each of the measurements from feet to inches by multiplying by .

Height:  inches

Sidelength of base:  inches

The base of the pyramid has area

square inches.

Substitute   into the volume formula:

cubic inches

### Example Question #5 : How To Find The Volume Of A Pyramid

The height of a right pyramid and the sidelength of its square base are equal. The perimeter of the base is 3 feet. Give its volume in cubic inches.

Explanation:

The perimeter of the square base,  feet, is equivalent to  inches; divide by  to get the sidelength of the base - and the height:  inches.

The area of the base is therefore  square inches.

In the formula for the volume of a pyramid, substitute :

cubic inches.

### Example Question #3 : How To Find The Volume Of A Pyramid

What is the volume of a pyramid with the following measurements?

Explanation:

The volume of a pyramid can be determined using the following equation:

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

The pyramid has a length, width, and height of  respectively.  What is the volume of the pyramid?

Explanation:

Write the formula for the volume of a pyramid.

Substitute the dimensions and solve.

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

If the base area of the pyramid is , and the height is , what is the volume of the pyramid?

Explanation:

Write the volume formula for the pyramid.

The base area is represented by .

Substitute the knowns into the formula.

### Example Question #5 : Volume Of A Pyramid

Find the volume of a pyramid with a length of 4, width of 7, and a height of 3.

Explanation:

Write the formula to find the area of a pyramid.

Substitute the dimensions.

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

Find the volume of a pyramid if the length, base, and height are  respectively.