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Originally Posted by Manoel
Sanddrag,
You don't need any volume information at all. Use your second formula and take the partial derivative of A in respect to r, set it to zero and you'll achieve the desired result (except for a nasty negative sign - maybe it's irrelevant, maybe I did something wrong!  ). To prove it's a minimum point, take the second partial derivative - you get a positive constant, thus, it is indeed a minimum point. 
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if you try deriving just the second equation, then h is a variable, and you end up with a dh/dr term that you need a value for. substituting from the volume equation gets rid of this term because V is a constant in this case.
sanddrag: V is a constant in this case since you said yourself for a given volume treat it as another number. Thus:
A' = 4*pi*r - 2*V/r^2