Explanation Formula used: The volume of a sphere with radius r is given by, V = 4 3 π r 3 . Calculation: The given figure has a sphere inside thesphere. Observe that the diameter of the larger sphere is 14 in, which implies the radius is 7in. Observe that the diameter of the smaller sphere is 7 in, which implies the radius is 3.5 in. The volume of the shaded region is obtained by the subtracting the volume of the smaller sphere from the volume of the larger sphere. Compute the volume of thelarge sphere as follows. V = 4 3 π r 3 = 4 3 π ( 7 ) 3 = 1372 3 π ≈ 457.33 π in . 3 Thus, the volume of the cone is 457.33 π in 3 . The volume of the small sphere is, V = 4 3 π r 3 = 4 3 π ( 3.5 ) 3 = 171

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Author: Angel

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Chapter 8, Problem 30RE

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The volumes of the shaded region of the sphere.

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Chapter 8, Problem 29RE

Chapter 8, Problem 31RE

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The volumes of the shaded region of the sphere.

Solution Summary: The author explains the formula used to determine the volumes of the shaded region of a sphere.

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The volumes of the shaded region of the sphere.

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