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10.7: Surface Areas and Volumes of Spheres

10.7: Surface Areas and Volumes of Spheres. Objective: To find the surface area and volume of a sphere. Parts of a Sphere:. A sphere is the set of all points in space equidistant from a given point. The center of a sphere is the given point from which all points on the sphere

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10.7: Surface Areas and Volumes of Spheres

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  1. 10.7: Surface Areas and Volumes of Spheres Objective: To find the surface area and volume of a sphere

  2. Parts of a Sphere: A sphere is the set of all points in space equidistant from a given point. The center of a sphere is the given point from which all points on the sphere are equidistant.

  3. The radius of a sphere is a segment that has one endpoint at the center and the other endpoint on the sphere. The diameter of a sphere is a segment passing through the center with endpoints on the sphere

  4. Theorem 10.10: Surface Area of a Sphere FORMULA: SA = 4πr² Theorem 10.11: Volume of a Sphere V = 4/3πr³ FORMULA:

  5. Ex. #1: The circumference of a rubber ball is 13 cm. Find the surface area to the nearest whole number. What is missing? radius How do we find it? Use the circumference formula.

  6. Find r. C = 2πr 13 = 2(3.14)(r) 13 = 6.28r 2.07 = r SA = 4πr² = 4(3.14)(2.07)² = 54 cm²

  7. Ex #2: Find the volume of the sphere. Leave your answer in terms of π. V = 4/3πr³ = 4/3π(15)³ = 4500π cm3

  8. Ex. #3: The volume of a sphere is 4200 ft³. Find the surface area to the nearest tenth. What is missing? radius How do we find it? Use the volume formula.

  9. First find r. V = 4/3πr³ 4200 = 4/3πr³ 4200 = 4.19r3 1002.39 = r³ 10.01 = r Then find SA SA = 4πr² = 4(3.14)(10.01)² = 1258.5 ft²

  10. Assignment: Pg 560 # 2-18 even , 18-20, 24, 29-32

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