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                                      Michael Lee's Mathematics and Physics

The Surface Area of a Circle Derivation


I'm going to show three methods here.  The first method is the easiest; the second and third ones, involve trigonometric substitution and is based on Cartesian coordinates involving lengthy, complicated calculations.  All angle measurements are in radians.




First Method


                     Take any circle of radius r;  hold r constant and note the following...





Second Method



Now this is the tricky part...





                The third method.