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Michael Lee's Mathematics and Physics

The Surface Area of a Circle

 

I'm going to show two methods here.  The first one is based on Cartesian coordinates involving 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...

 

 

 

 

 

 

 

 

 

 

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