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:
= 
