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# Volume of Prisms and Pyramids Study Guide

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## Introduction to Volume of Prisms and Pyramids

### Lesson Summary

In this lesson, you will learn how to find the volume of prisms and pyramids using formulas.

Wen you are interested in finding out how much a refrigerator holds or the amount of storage space in a closet, you are looking for the volume of a prism. Volume is expressed in cubic units. Just like an ice tray is filled with cubes of ice, volume tells you how many cubic units will fit into a space.

## Volume of Prisms

Prisms can have bases in the shape of any polygon. A prism with a rectangle for its bases is called a rectangular prism. A prism with triangles for its bases is referred to as a triangular prism. A prism with hexagons as its bases is called a hexagonal prism, and so on. Prisms can be right or oblique. A right prism is a prism with its bases perpendicular to its sides, meaning they form right angles. Bases of oblique prisms do not form right angles with their sides. An example of an oblique prism is the Leaning Tower of Pisa. In this lesson, you will concentrate on the volume of right prisms. When we refer to prisms in this lesson, you can assume we mean a right prism.

The volume of a rectangular prism could also be stated in another way. The area of the base of a rectangular prism is the length times the width, the same length and width used with the height to find the volume—in other words, the area of the base (B) times the height. This same approach can also be applied to other solid figures. In Lesson 13, you studied ways to find the area of most polygons, but not all. However, if you are given the area of the base and the height of the figure, then it is possible to find its volume. Likewise, if you do know how to find the area of the base (B), use the formula for that shape, then multiply by the height (h) of the figure.

#### Examples:

Find the volume of each prism.

## Volume of a Cube

Recall that the edges (e) of a cube all have the same measurement; therefore, if you replace the length (l ), width (w), and height (h) with the measurement of the edge of the cube, then you will have the formula for the volume of the cube, V = e3.

Example: Find the volume of the cube.

## Volume of a Pyramid

A polyhedron is a three-dimensional figure whose surfaces are all polygons. A regular pyramid is a polyhedron with a base that is a regular polygon and a vertex point that lies directly over the center of the base.

If you have a pyramid and a rectangular prism with the same length, width, and height, you would find that it would take three of the pyramids to fill the prism. In other words, one-third of the volume of the prism is the volume of the pyramid.

#### Examples:

Find the volume of each pyramid.

Practice problems for these concepts can be found at: Volume of Prisms and Pyramids Practice Questions.

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