Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Find the area of each figure described. Use 3.14 for p. 1. a triangle with a base of 6 feet and a height of 3 feet 2. a circle with radius 5 in. 9 ft2 78.5 in2

Problem of the Day You are painting identical wooden cubes red and blue. Each cube must have 3 red faces and 3 blue faces. How many cubes can you paint that can be distinguished from one another? only 2

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

Check It Out: Example 1A Find the volume of the figure to the nearest tenth. Use 3.14 for . A rectangular prism with base 5 mm by 9 mm and height 6 mm. B = 5 • 9 = 45 mm2 Area of base V = Bh Volume of prism = 45 • 6 = 270 mm3

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

Check It Out: Example 1C Find the volume of the figure to the nearest tenth. Use 3.14 for . B = • 12 • 10 1 2 Area of base 10 ft = 60 ft2 V = Bh Volume of a prism 14 ft = 60(14) = 840 ft3 12 ft

Additional Example 2A: Exploring the Effects of Changing Dimensions A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling the length, width, or height of the box would triple the amount of juice the box holds. The original box has a volume of 24 in3. You could triple the volume to 72 in3 by tripling any one of the dimensions. So tripling the length, width, or height would triple the amount of juice the box holds.

Additional Example 2B: Exploring the Effects of Changing Dimensions A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling the height of the can would have the same effect on the volume as tripling the radius. By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.

Check It Out: Example 2 A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume. The original cylinder has a volume of 4 • 3 = 12 cm3. V = 36 • 3 = 108 cm3 By tripling the radius, you would increase the volume nine times.

Check It Out: Example 2 Continued The original cylinder has a volume of 4 • 3 = 12 cm3. V = 4 • 9 = 36 cm3 Tripling the height would triple the volume.

Additional Example 3: Music Application A drum company advertises a snare drum that is 4 inches high and 12 inches in diameter. Estimate the volume of the drum. d = 12, h = 4 d 2 12 2 r = = = 6 V = (r2)h Volume of a cylinder. = (3.14)(6)2 • 4 Use 3.14 for p. = (3.14)(36)(4) = 452.16 ≈ 452 The volume of the drum is approximately 452 in3.

Check It Out: Example 3 A drum company advertises a bass drum that is 9 inches high and 19 inches in diameter. Estimate the volume of the drum. d = 19, h = 9 d 2 19 2 r = = = 9.5 V = (r2)h Volume of a cylinder. = (3.14)(9.5)2 • 9 Use 3.14 for . = (3.14)(90.25)(9) = 2550.465 ≈ 2550 The volume of the drum is approximately 2,550 in3.

Additional Example 4: Finding the Volume of Composite Figures Find the volume of the the barn. Volume of barn Volume of rectangular prism Volume of triangular prism + = V = (40)(50)(15) + (40)(10)(50) 1 2 = 30,000 + 10,000 = 40,000 ft3 The volume is 40,000 ft3.

Find the volume of the house. Check It Out: Example 4 Find the volume of the house. Volume of house Volume of rectangular prism Volume of triangular prism + = = (8)(3)(4) + (5)(8)(3) 1 2 5 ft = 96 + 60 4 ft V = 156 ft3 8 ft 3 ft

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 22

Lesson Quiz 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.

Lesson Quiz for Student Response Systems 1. Identify the volume of the cylinder to the nearest tenth. Use 3.14 for . A. 1099 in3 B. 1582.6 in3 C. 1356.5 in3 D. 1846.3 in3 24

Lesson Quiz for Student Response Systems 2. Identify the volume of the rectangular prism to the nearest tenth. A. 338 m3 B. 390 m3 C. 364 m3 D. 422.5 m3 25

Lesson Quiz for Student Response Systems 3. Explain whether doubling the height of a rectangular prism will double the volume. A. Yes; the volume would be doubled because you have to use the height to find the volume. B. No; the volume would be tripled because you have to use height to find the volume. C. No; the volume would be tripled because you have to use the square of the height to find the volume. D. Yes; the volume would be doubled because you have to use the square of the height to find the volume. 26