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 $$S = \int_{a}^{\,b} {2\pi [c-f(x)] \sqrt{1+[f'(x)]^2}}\, dx.$$ Use this formula and a computer algebra system to find the area of the surface generated by rotating the curve $y=\sqrt{x},\; 0 \le x \le 4,$ about the line $y=4.$

Surface area =