The formula for the area of a spherical cap with radius (the sphere's radius) $\displaystyle R$ and height $\displaystyle h$ is given as

$\displaystyle A = 2{\pi}Rh$

This formula can be expressed in terms of $\displaystyle R$ and $\displaystyle r$, where $\displaystyle r$ is the radius of the base of the spherical cap:

$\displaystyle (R-h)^2 + r^2 = R^2$

$\displaystyle (R-h)^2 = R^2 - r^2$

$\displaystyle R-h = \sqrt{R^2 - r^2}$

$\displaystyle h = R - \sqrt{R^2 - r^2}$

$\displaystyle A = 2{\pi}R(R - \sqrt{R^2 - r^2})$

Now, how do I express the formula in terms of $\displaystyle R^2$ and $\displaystyle \frac{r}{R}$? I've been trying for quite some time but I'm stuck...