A geometry problem by W Rose

Geometry Level 3

Two right circular cones each share the same altitude and a height of \(h\). One cone has a base of radius \(R\) and the other cone is inverted and has a base of radius \(r\) as shown in the figure below.

The volume of the region common to both cones can be calculated by the formula:

\[V =\frac {\pi R^2 r^2 h}{ X ( R + r )^2} \]

Find \(X\).

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