Preview Warm Up California Standards Lesson Presentation

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

California Standards MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Also covered: MG2.4

Vocabulary volume

The volume of a three-dimensional figure is the number of cubes it can hold. Each cube represents a unit of measure called a cubic unit.

Height Height Height Base Base Base Triangular prism Rectangular prism Cylinder Height Height Height Base Base Base

Additional Example 1: Finding the Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. A. B = 4 • 12 = 48 ft2 The base is a rectangle. V = Bh Volume of a prism = 48 • 4 Substitute for B and h. = 192 ft3 Multiply.

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

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

Find the volume of the figure to the nearest tenth. Use 3.14 for . A. Check It Out! Example 1 Find the volume of the figure to the nearest tenth. Use 3.14 for . A. 10 in. 6 in. 3 in. B = 6 • 3 = 18 in.2 The base is a rectangle. V = Bh Volume of prism = 18 • 10 Substitute for B and h. = 180 in3 Multiply.

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

Check It Out! Example 1 Find the volume of the figure to the nearest tenth. C. B = • 12 • 10 1 2 The base is a triangle. 10 ft = 60 ft2 V = Bh Volume of a prism 14 ft = 60(14) Substitute for B and h. = 840 ft3 Multiply. 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 only 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 only 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 9 times the original volume.

Check It Out! Example 2A A box measures 5 in. by 3 in. by 7 in. Explain whether tripling only the length, width, or height of the box would triple the volume of the box. The original box has a volume of (5)(3)(7) = 105 cm3. V = (15)(3)(7) = 315 cm3 Tripling the length would triple the volume.

Check It Out! Example 2A Continued The original box has a volume of (5)(3)(7) = 105 cm3. V = (5)(3)(21) = 315 cm3 Tripling the height would triple the volume.

Check It Out! Example 2A Continued The original box has a volume of (5)(3)(7) = 105 cm3. V = (5)(9)(7) = 315 cm3 Tripling the width would triple the volume.

Check It Out! Example 2B A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling only 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 2B 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 12 inches high and 28 inches in diameter. Estimate the volume of the drum. d = 28, h = 12 d 2 28 2 r = = = 14 V = (r2)h Volume of a cylinder = (3.14)(14)2 • 12 Use 3.14 for . = (3.14)(196)(12) = 7385.28 ≈ 7,385 The volume of the drum is approximately 7,385 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 of the barn is 40,000 ft3.

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

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.