So, I have been trying to figure out how to derive the equation for the surface area of a sphere. All attempts have resulted in colossal failure and as such are not even worth posting on the forum. I know Archimedes was the first to come up with the formula but I have not been able to find something on the web that goes into a detailed proof that is understandable. There are of course several sites that detail a circumscribed sphere in a cylinder of height equal to twice the radius of the sphere and how it has the same surface area (not including end caps) but how was that connection made? I am interested in any solutions (*EDIT* - no calculus) not just that of Archimedes.