1. Volumes of Prisms and Surface Area #31

2. 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.

3. Example 1 Find the volume of the rectangular prism.

4. Example 2 Find the volume of each rectangular prism.

5. 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.

6. Example 3 Find the volume of the triangular prism.

7. FYI The bases of a prism are always two congruent, parallel polygons. Caution!

8. Example 4

9. 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.

10. Example 1 Find the surface area S of the prism. Method 1: Use a net.

11. Example 2 Find the surface area S of each prism. Method 2: Use a three-dimensional drawing.

12. 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.

13. Example 3 Find the surface area S of the pyramid.

14. 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

15. Example 4 Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.