Your browser version is outdated. We recommend that you update your browser to the latest version.

                                      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.