Warm Up Find the area of each figure described. Use 3.14 for pi. 1.

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Warm Up Find the area of each figure described. Use 3.14 for pi. 1. 2. a circle with radius 5 in.

Words Numbers Formula VOLUME OF CYLINDERS Cylinder: The volume of a cylinder is the area of the base B times the height h. B =  (22) V = Bh = 4 units2 = (r2)h V = (4)(6) = 24  75.4 units3 Area is measured in square units. Volume is measured in cubic units. Remember!

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

Check It Out: Example 1B Find the volume of the figure to the nearest tenth. Use 3.14 for . B =  (82) Area of base 8 cm = 64 cm2 V = Bh Volume of a cylinder 15 cm = (64)(15) = 960  3,014.4 cm3

Find the volume of each figure to the nearest tenth. Use 3.14 for π. 1. 10 in. 12 in. 2. Explain whether doubling the radius of the cylinder above will double the volume.

VOLUME OF CONES

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 1B Find the volume of the figure. Use 3.14 for p. B = (32) = 9 m2 7 m 1 3 V = • 9 • 7 V = Bh 1 3 3 m V = 21  65.9 m3 Use 3.14 for .

Lesson Quiz: Part 1 Find the volume of each figure to the nearest tenth. Use 3.14 for p. 2. the cone 78.5 in3

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.

The volume of a hemisphere is exactly halfway between the volume of a cone and a cylinder with the same radius r and height equal to r.

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

4 V = pr3 3 Volume of a sphere 4 = p(3)3 3 Substitute 3 for r. Check It Out: Example 1 Find the volume of a sphere with radius 3 m, both in terms of p and to the nearest tenth. Use 3.14 for p. 4 3 V = pr3 Volume of a sphere = p(3)3 4 3 Substitute 3 for r. = 36p m3  113.0 m3

Lesson Quiz: Part I Find the volume of each sphere, both in terms of  and to the nearest tenth. Use 3.14 for p. 1. r = 4 ft 2. d = 6 m 85.3p ft3, 267.8 ft3 36p m3, 113.0 m3 3. A basketball has a circumference of 29 in. To the nearest cubic inch, what is its volume?

Find the volume of each figure. Use 3.14 for p. Cylinder with a height of 3 in and a radius of 2 in Cone with a height of 3 in and a radius of 2 in Sphere with a radius of 2 in Homework: Workbook pages 60-61, 64 (VOLUME of cylinders, cones, and spheres ONLY)