Ball & Dome

Geometry Level 3

A sweets shop sells candies in 2 different styles: a spherical ball and a dome. The dome-like shape is a spherical section of a larger sphere with height hh and base radius R,R, as shown above, while the candy ball has radius rr with 2r=R+h2r = R + h.

If both shapes have the same total surface area, what is the ratio Rh\frac{R}{h}?

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