Problem #181

A water glass is a truncated right circular cone (a "frustum"). The radius of the upper circle is R, the radius of the lower circle is r, and the height is h. The glass is filled with water and tilted until the surface of the water runs from the edge of the top rim to the edge of the bottom of the glass as shown in the figure below (perspective view on the left, side view on the right).

What fraction of the total volume of the water glass consists of water? For example, if R = r, the glass is cylindrical and the fraction is 1/2.

The solution will be posted shortly.

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