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Spheres 8-9 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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Spheres 8-9 Warm Up 1. Find the surface area of a square pyramid whose base is 3 m on a side and whose slant height is 5 m. 2. Find the surface area of a cone whose base has a radius of 10 in. and whose slant height is 14 in. Use 3.14 for . 39 m 2 753.6 in 2

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Spheres 8-9 Problem of the Day Find the slant height of the cone with the following measurements: The area of its base is one-third of its total surface area. The radius is 4 cm. 8 cm

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Spheres 8-9 Learn to find the volume and surface area of spheres.

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Spheres 8-9 Vocabulary sphere hemisphere great circle

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Spheres 8-9 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.

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Spheres 8-9 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.

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Spheres 8-9

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Spheres 8-9 Additional Example 1: Finding the Volume of a Sphere Find the volume of a sphere with radius 12 cm, both in terms of and to the nearest tenth. Use 3.14 for . = 2304 cm 3 7,234.6 cm 3 Volume of a sphere Substitute 12 for r. 4343 V = r 3 = (12) 3 4343

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Spheres 8-9 Check It Out: Example 1 Find the volume of a sphere with radius 3 m, both in terms of and to the nearest tenth. Use 3.14 for . = 36 m 3 113.0 m 3 Volume of a sphere Substitute 3 for r. 4343 V = r 3 = (3) 3 4343

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Spheres 8-9 The surface area of a sphere is four times the area of a great circle.

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Spheres 8-9 Additional Example 2: Finding Surface Area of a Sphere Find the surface area, both in terms of and to the nearest tenth. Use 3.14 for . = 36 in 2 113.0 in 2 S = 4r 2 = 4(3 2 ) Surface area of a sphere Substitute 3 for r.

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Spheres 8-9 Check It Out: Example 2 The moon has a radius of 1738 km. Find the surface area, both in terms of and to the nearest tenth. Use 3.14 for . = 12,082,576 km 2 37,939,288.6 km 2 S = 4r 2 = 4(1738 2 ) Surface area of a sphere Substitute 1738 for r. 1738 km

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Spheres 8-9 Additional Example 3: Comparing Volumes and Surface Areas Sphere: 310,464 cm 3 Rectangular Prism: = (44)(84)(84) = 310,464 cm 3 V = lwh V = r 3 = (42 3 ) 4343 4343 74,088 22 7 4343 Compare the volumes and surface areas of a sphere with radius 42 cm with that of a rectangular prism measuring 44 cm by 84 cm by 84 cm.

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Spheres 8-9 S = 4r 2 = 4(42 2 ) = 7,056 = 28,896 cm 2 S = 2(44)(84) + 2(44)(84) + 2(84)(84) Additional Example 3 Continued Sphere: Rectangular Prism: S = 2lw + 2lh + 2wh 7,056 22,176 cm 2 22 7 The sphere and the prism have approximately the same volume, but the prism has a larger surface area.

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Spheres 8-9 Check It Out: Example 3 Sphere: 38,808 mm 3 Rectangular Prism: = (22)(42)(42) = 38,808 mm 3 V = lwh V = r 3 = (21 3 ) 4343 4343 9261 22 7 4343 Compare the volume and surface area of a sphere with radius 21 mm with that of a rectangular prism measuring 22 by 42 by 42 mm.

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Spheres 8-9 S = 4r 2 = 4(21 2 ) = 1764 = 7224 mm 2 S = 2(22)(42) + 2(22)(42) + 2(42)(42) Sphere: Rectangular Prism: S = 2lw + 2lh + 2wh 1764 5544 mm 2 22 7 The sphere and the prism have approximately the same volume, but the prism has a larger surface area. Check It Out: Example 3 Continued

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Spheres 8-9 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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Spheres 8-9 Lesson Quiz: Part I Find the volume of each sphere, both in terms of and to the nearest tenth. Use 3.14 for . 1. r = 4 ft 2. d = 6 m Find the surface area of each sphere, both in terms of and to the nearest tenth. Use 3.14 for . 36m 3, 113.0 m 3 85.3ft 3, 267.8 ft 3 2.25 mi 2, 7.1 mi 2 1936 in 2, 6079.0 in 2 3. r = 22 in 4. d = 1.5 mi

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Spheres 8-9 5. A basketball has a circumference of 29 in. To the nearest cubic inch, what is its volume? Lesson Quiz: Part II 412 in 3

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Spheres 8-9 1. Find the volume of a sphere with radius 5 ft, both in terms of and to the nearest tenth. Use 3.14 for . A. 166.7ft 3, 523.3 ft 3 B. 166.7ft 3, 576.5 ft 3 C. 183.6ft 3, 576.5 ft 3 D. 183.6ft 3, 523.3 ft 3 Lesson Quiz for Student Response Systems

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Spheres 8-9 2. Find the volume of a sphere with a diameter of 8 m, both in terms of and to the nearest tenth. Use 3.14 for . A. 682.7m 3, 2143.6 m 3 B. 682.7m 3, 267.9 m 3 C. 85.3m 3, 2143.6 m 3 D. 85.3m 3, 267.9 m 3 Lesson Quiz for Student Response Systems

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Spheres 8-9 3. A decorative lamp in the form of a sphere has a circumference of 32 inches. To the nearest cubic inch, what is its volume? A. 554in 3 B. 562in 3 C. 571in 3 D. 580in 3 Lesson Quiz for Student Response Systems

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