Chapter 10: Area & Volume

10.4, 10.5, 10.6Space Figures

Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres

Space Figures• common three-dimensional figures

• prisms: two parallel bases that are congruent polygons, lateral faces that are parallelograms

Space Figures

• Pyramids:base that is a polygon, lateral faces are triangles

• Cylinders:two parallel bases that are congruent circles

Space Figures

• Cones: one circular base and one vertex

• Sphere: set of all points in space that are a given distance from a given point called the center

Example 1• For each figure, describe the bases and name

the figure.

Example 2

• Name the space figure you can form from each net:

Example 2a• Name the space figure you can form from each

net:

Surface Area

• abbreviated S.A.

• sum of the areas of the base(s) and the lateral faces of a space figure

• one way to find it: find the area of each piece of the space figure’s net

Example 1

• Find the surface area of the rectangular prism using a net.

8 in

5 in20 in

Example 1a

• Find the surface area of the triangular prism:6 yd

5 yd

4 yd

3 yd

Example 2

• Find the surface area of the triangular prism at the right.

12 cm

5 cm

6 cm

4 cm5 cm

Surface Area of a Prism

• lateral area: LA = ph– perimeter of base times height

• surface area: SA = LA + 2B– lateral area plus the area of the two bases

Surface Area of a Cylinder

• lateral area: LA = 2πrh– twice pi times the radius of the base times the

height

• surface area: SA = LA + 2B

Example 3

• Find the surface area of the can:

11.5 cm

7 cm

Example 3a

• Find the surface area of a can with radius 5 cm and height 20 cm.

Surface Area of a Pyramid

• lateral area: LA = ½ pl– ½ perimeter of the base times the slant height

• surface area: SA = LA + B– lateral area plus the area of the base

Example 1

• Find the surface area of the square pyramid:

16 cm

12 cm12 cm

Surface Area of a Cone

• lateral area: LA = πrl– pi times radius times slant height

• surface area: SA = LA + B– lateral area plus area of the base

Example 2

• Find the surface area of the cone:

4 cm

10 cm

Surface Area of a Sphere

24 rSA

Example 3

• Calculate the surface area of a basketball:

10 in

Homework

• p. 541: 2-12 even, 21-23

• p. 548: 4-12 all

• p. 555: 1-12 all