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 \(h\) and base radius \(R,\) as shown above, while the candy ball has radius \(r\) with \(2r = R + h\).

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

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