# 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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