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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. 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.

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 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 m2 753.6 in2

  3. 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

  4. Learn to find the volume and surface area of spheres.

  5. Vocabulary sphere hemisphere great circle

  6. 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 hemisphereis agreat circle.

  7. 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.

  8. 4 3 V = pr3 = p(12)3 4 3 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. Volume of a sphere Substitute 12 for r. = 2304p cm3 7,234.6 cm3

  9. 4 3 V = pr3 = p(3)3 4 3 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. Volume of a sphere Substitute 3 for r. = 36p m3 113.0 m3

  10. The surface area of a sphere is four times the area of a great circle.

  11. Additional Example 2: Finding Surface Area of a Sphere Find the surface area, both in terms of p and to the nearest tenth. Use 3.14 for p. Surface area of a sphere S = 4pr2 = 4p(32) Substitute 3 for r. = 36p in2 113.0 in2

  12. 1738 km Check It Out: Example 2 The moon has a radius of 1738 km. Find the surface area, both in terms of p and to the nearest tenth. Use 3.14 for p. S = 4pr2 Surface area of a sphere = 4p(17382) Substitute 1738 for r. = 12,082,576p km2  37,939,288.6 km2

  13. V = pr3= p(423) 22 7  74,088 4 3 4 3 4 3 Additional Example 3: Comparing Volumes and Surface Areas 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. Rectangular Prism: Sphere: V = lwh = (44)(84)(84) 310,464 cm3 =310,464 cm3

  14. 22 7 S = 2(44)(84) + 2(44)(84)  7,056  22,176 cm2 + 2(84)(84) Additional Example 3 Continued Rectangular Prism: Sphere: S = 4pr2 = 4p(422) S = 2lw + 2lh + 2wh = 7,056p = 28,896 cm2 The sphere and the prism have approximately the same volume, but the prism has a larger surface area.

  15. V = pr3= p(213) 22 7  9261 4 3 4 3 4 3 Check It Out: Example 3 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. Rectangular Prism: Sphere: V = lwh = (22)(42)(42) 38,808 mm3 =38,808 mm3

  16. 22 7 S = 2(22)(42) + 2(22)(42)  1764  5544 mm2 + 2(42)(42) Check It Out: Example 3 Continued Rectangular Prism: Sphere: S = 4pr2 = 4p(212) S = 2lw + 2lh + 2wh = 1764p = 7224 mm2 The sphere and the prism have approximately the same volume, but the prism has a larger surface area.

  17. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  18. 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 Find the surface area of each sphere, both in terms of  and to the nearest tenth. Use 3.14 for p. 85.3p ft3, 267.8 ft3 36p m3, 113.0 m3 1936p in2, 6079.0 in2 3.r = 22 in 4.d = 1.5 mi 2.25p mi2, 7.1 mi2

  19. Lesson Quiz: Part II 5.A basketball has a circumference of 29 in. To the nearest cubic inch, what is its volume? 412 in3

  20. Lesson Quiz for Student Response Systems 1. Find the volume of a sphere with radius 5 ft, both in terms of p and to the nearest tenth. Use 3.14 for p. A. 166.7p ft3, 523.3 ft3 B. 166.7p ft3, 576.5 ft3 C.183.6p ft3, 576.5 ft3 D.183.6p ft3, 523.3 ft3

  21. Lesson Quiz for Student Response Systems 2. Find the volume of a sphere with a diameter of 8 m, both in terms of p and to the nearest tenth. Use 3.14 for p. A. 682.7p m3, 2143.6 m3 B. 682.7p m3, 267.9 m3 C.85.3p m3, 2143.6 m3 D.85.3p m3, 267.9 m3

  22. Lesson Quiz for Student Response Systems 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. 554in3 B. 562in3 C.571in3 D.580in3

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