Refer to the figure above, where we've sliced the original picture down the middle.  Here .   If we maximize this figure in terms of , we just need to double that to find .



 = 

 = 



Observe:

 





Substituting for r and h:

 = 

 = 



 = 

=  + 



...factoring out 

=    (*)



Now take the derivative of  with respect to :



 = 

   

= 



... substitute  ...

=   





This last function is zero at approx.   = 2.575rad, = 5.716rad, ...



By graphing, one can see 2.575rad  results in a maximum area, while 5.716 results in a minimal area.   



2.575rad is approx 147.54degrees.



Ans:  =  maximizes the total area.



Just in case...

If you were interested in the value of the total maximal area, note that you would need a modified form of (*) because that equation computes 1/2 of the total area:

  =     

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