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Michael Lee's Mathematics and Physics

The Surface Area of a Circle Derivation

 

I'm going to show two methods here.  The first one, called trigonometric substitution, is based on Cartesian coordinates involving lengthy, complicated calculations and the other involves simple geometry.

 

First Method Using Trigonometric Substitution

 

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

 

 

 

 

 

 

Now this is the tricky part...

 

 

 

 

                Whew, that was exciting!  There must be a better way...