A right circular cone is placed with the wide, circular side on a table so that the vertex (the sharp point) is up. Assume that

Question

A right circular cone is placed with the wide, circular side on a table so that the vertex (the sharp point) is up. Assume that the cone is 28 inches high, and that the radius of the circular base is 21 inches. Next, cut off the top of the cone (cutting parallel to the table) at a height which creates a circular cross section of radius 12 inches. You now have what is known as a "truncated" cone. Imagine now that you have a lampshade in the shape of this truncated cone. Inside the lampshade is a spherical plastic ball that houses the light bulb. The spherical plastic ball is completely inside the lampshade, and the ball is tangent to both the circular top and to the circular bottom of the lampshade. Find: 
(a) The volume of the lamp shade.
(b) The volume of the spherical plastic ball. 
(c) The volume of the part of the lampshade that is not occupied by the spherical plastic ball.

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