Volumes of Prisms and

Surface Area

#31

Vocabulary

Volume is the number of cubic units needed to fill a space. V = lwh

Ex:Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cm3.

Example 1

Find the volume of the rectangular prism.

Example 2

Find the volume of each rectangular prism.

FYI

To find the volume of any prism, you can use the formula V= Bh, where B is the area of the base, and h is the prism’s height.

Example 3

Find the volume of thetriangular prism.

FYI

The bases of a prism are always two congruent, parallel polygons.

Caution!

Example 4

Vocabulary

The surface area of a three-dimensional figure is the sum of the areas of its surfaces. To help you see all the surfaces of a three-dimensional figure, you can use a net. A net is the pattern made when the surface of a three-dimensional figure is layed out flat showing each face of the figure.

Example 1

Find the surface area S of the prism.

Method 1: Use a net.

Example 2

Find the surface area S of each prism.

Method 2: Use a three-dimensional drawing.

FYI

The surface area of a pyramid equals the sum of the area of the base and the areas of the triangular faces. To find the surface area of a pyramid, think of its net.

Example 3

Find the surface area S of the pyramid.

FYI

The surface area of a cylinder equals the sum of the area of its bases and the area of its curved surface.

To find the area of the curved surface of a cylinder, multiply its height by the circumference of the base.

Helpful Hint

Example 4

Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.