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Math Help - A maximum/minimum problem

  1. #1
    Junior Member
    Joined
    Nov 2009
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    45

    A maximum/minimum problem

    Prove that a closed cylinder of fixed surface area has maximum volume when its diameter equals its height

    For this question I have two equations,

    V = (pi)r^2h
    AND
    SA = 2(pi)r^2+2(pi)rh which equals a constant, or C

    Could someone help me find an equation to find the maximum volume and prove that it would be when diameter equals height?

    Thankyou =)
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  2. #2
    Junior Member Evales's Avatar
    Joined
    Oct 2007
    Posts
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    If the SA is constant then when you differentiate it the constant will become zero. Try manipulating the equation after you differentiate it.
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