# Surface Area of a Sphere without double integral

by cwbullivant
Tags: double, integral, sphere, surface
 P: 37 Is it possible to come up with a derivation of the surface area of a sphere without using a double integral? Most of the ones I've found seem to involve double integrals; For example, this was given as the "simplest" explanation in a thread from 2005: $$S=\iint dS=R^{2}\int_{0}^{2\pi}d\varphi \int_{0}^{\pi} d\vartheta \ \sin\vartheta$$ I was thinking about using shell integration for it, but as I recall, shell integration and solids of revolution deal only in volumes, not surface areas (This was by far my weakest area of Calc II, FWIW). I'm going to be doing double integrals fairly soon, but I wanted to know if there was a more simplistic method so I wouldn't have to wait until then.