Warm-up The base length is 30 cm.

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Presentation transcript:

Warm-up The base length is 30 cm. EQ: How do I solve real world problems involving cylinders, cones, and spheres? Warm-up 1.) Find the missing side. The height of the triangle is 20 inches. 25 cm 25 cm The base length is 30 cm. x cm

A cylinder is a three-dimensional figure that has two congruent circular bases.

Volume of Cylinders Words Numbers Formula Cylinder: The volume of a cylinder is the area of the base B times the height h. B =  (22) V = Bh = 4 units2 V = (r2)h V = (4)(6) = 24  75.4 units3

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

Example 1: Finding the Volume of Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . Volume of a cylinder formula V =  r2 h 4 in. V =  • 42 • 12 Substitute 12 in. Solve V =  • 16 • 12 V = 192 V  603.2 in3 Terms of pi

Example 2: Volume of Cylinders 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

Example 3: Volume of Cylinders 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 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.

Example 4: Volume of Cylinders 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 in.2

Example 5: Volume of Cylinders 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 in.2

Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for . 10 in. 1. 12 in. 942 in3