28. Visualization The region enclosed by the semicircle below is revolved completely about the x-axis.

    

    1. Describe the solid of revolution that is formed.
    2. Find its volume in terms of π.
    3. Find its surface area in terms of π.
29. Think About a Plan A cylindrical tank with diameter 20 in. is half filled with water. How much will the water level in the tank rise if you place a metallic ball with radius 4 in. in the tank? Give your answer to the nearest tenth.
    • What causes the water level in the tank to rise?
    • Which volume formulas should you use?

30. The sphere below fits snugly inside a cube with 6-in. edges. What is the approximate volume of the space between the sphere and cube?

    

    1. 28.3  in . 3 28.3 , in , . cubed
    2. 76.5  in . 3 76.5 , in , . cubed
    3. 102.9  in . 3 102.9 , in , . cubed
    4. 113.1  in . 3 113.1 , in , . cubed
31. Meteorology On September 3, 1970, a hailstone with diameter 5.6 in. fell at Coffeyville, Kansas. It weighed about 0.018  lb  / in . 3 0.018 , lb , slash , in , . cubed  compared to the normal 0.033  lb  / in . 3 0.033 , lb , slash , in , . cubed  for ice. About how heavy was this Kansas hailstone?
32. Reasoning Which is greater, the total volume of three spheres, each of which has diameter 3 in., or the volume of one sphere that has diameter 8 in.?
33. Reasoning How many great circles does a sphere have? Explain.

Find the volume in terms of π of each sphere with the given surface area.

34. 4 π  m 2 4 pi , m squared
35. 36 π  in . 2 36 pi . in , . squared
36. 9 π  ft 2 9 pi , ft squared
37. 100 π  mm 2 100 pi , mm squared
38. 25 π  yd 2 25 pi , yd squared
39. 144 π  cm 2 144 pi , cm squared
40. 49 π  m 2 49 pi , m squared
41. 225 π  mi 2 225 pi , mi squared
42. Recreation A spherical balloon has a 14-in. diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the balloon remains a sphere.
    1. Find the volume of the fully inflated balloon in terms of π.
    2. Find the volume of the half-inflated balloon in terms of π.
    3. What is the diameter of the half-inflated balloon to the nearest inch?
43. Sports Equipment The diameter of a golf ball is 1.68 in.
    1. Approximate the surface area of the golf ball.

    2. Reasoning Do you think that the value you found in part (a) is greater than or less than the actual surface area of the golf ball? Explain.

       

Geometry in 3 Dimensions A sphere has center (0, 0, 0) and radius 5.

44. Name the coordinates of six points on the sphere.
45. Tell whether each of the following points is inside, outside, or on the sphere.
    1. A ( 0 , − 3 , 4 ) eh open 0 comma negative 3 comma 4 close
    2. B ( 1 , − 1 , − 1 ) b open 1 comma negative 1 comma negative 1 close
    3. C ( 4 , − 6 , − 10 ) c open 4 comma negative 6 comma negative 10 close

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