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Unread 13-03-2005, 21:11
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Re: Proving smallest surface area of cylinder is when h=2r

Quote:
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.
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
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