Ball & Dome

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 $\frac{R}{h}$?