Warm UP The playhouse is a composite figure with a floor and no windows. What is the surface area of the playhouse?

Additional Example 3 Continued 2 Make a Plan Draw nets of the figures and shade the parts that show the surface area of the playhouse.

The surface area of a sphere is four times the area of a great circle.

Additional Example 2: Finding Surface Area of a Sphere Find the surface area, both in terms of p and to the nearest tenth. Use 3.14 for p. S = 4pr2 Surface area of a sphere = 4p(32) Substitute 3 for r. = 36p in2  113.0 in2

Learn to find the volume of prisms and cylinders.

Area is measured in square units. Volume is measured in cubic units. Remember!

Additional Example 1A: Finding the Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. Use 3.14 for . a rectangular prism with base 2 cm by 5 cm and height 3 cm B = 2 • 5 = 10 cm2 Area of base V = Bh Volume of a prism = 10 • 3 = 30 cm3

Additional Example 1B: Finding the Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . B =  (42) = 16 in2 Area of base 4 in. V = Bh Volume of a cylinder 12 in. = 16 • 12 = 192  602.9 in3

Additional Example 1C: Finding the Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . B = • 6 • 5 = 15 ft2 1 2 Area of base 5 ft V = Bh Volume of a prism = 15 • 7 = 105 ft3 7 ft 6 ft

Warm UP (You can use a calculator) Find the volume of each figure to the nearest tenth. Use 3.14 for . 10 in. 1. 2. 3. 2 in. 12 in. 12 in. 10.7 in. 15 in. 3 in. 8.5 in. 942 in3 306 in3 160.5 in3 4. Explain whether doubling the radius of the cylinder above will double the volume. No; the volume would be quadrupled because you have to use the square of the radius to find the volume.

Learn to find the volume of pyramids and cones.

Additional Example 1A: Finding the Volume of Pyramids and Cones Find the volume of the figure. Use 3.14 for p. B = (4 • 7) = 14 cm2 1 2 1 3 V = • 14 • 6 V = Bh 1 3 V = 28 cm3

Additional Example 1B: Finding the Volume of Pyramids and Cones Find the volume of the figure. Use 3.14 for p. B = (32) = 9 in2 1 3 V = • 9 • 10 V = Bh 1 3 V = 30  94.2 in3 Use 3.14 for .

Check It Out: Example 1A Find the volume of the figure. Use 3.14 for p. B = (5 • 7) = 17.5 in2 1 2 7 in. 1 3 V = • 17.5 • 7 V = Bh 1 3 5 in. 7 in. V  40.8 in3

Learn to find the volume and surface area of spheres.

A sphere is the set of points in three dimensions that are a fixed distance from a given point, the center. A plane that intersects a sphere through its center divides the two halves or hemispheres. The edge of a hemisphere is a great circle.

Additional Example 1: Finding the Volume of a Sphere Find the volume of a sphere with radius 12 cm, both in terms of p and to the nearest tenth. Use 3.14 for p. 4 3 V = pr3 Volume of a sphere = p(12)3 4 3 Substitute 12 for r. = 2304p cm3  7,234.6 cm3