If the curve $y=f(x),\;a \le x \le b,$ is rotated about the horizontal line $y=c,$ where $f(x) \le c,$ then one can prove that a formula for the area of the resulting surface is $$S = \int_{a}^{\,b} {2\pi [c-f(x)] \sqrt{1+[f'(x)]^2}}\, dx.$$

Find the area of the surface generated by rotating the circle $x^2+y^2=r^2$ about the line $y=r.$

Surface area =