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Math Help - Finding Minimum Surface Area

  1. #1
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    Finding Minimum Surface Area

    So I have gotten the equation for the total surface area of a cylinder in term of its radius as:

    T.S.A.=2\pi r^2+\frac{810}{r}

    Where does one begin to even find the minimum surface area of this cylinder? I have to find the minimum surface area graphically on where it appears to have minimum as well as through algebraic (optimisation) methods.

    Help appreciated, thanks.
    Last edited by NewUser01; July 17th 2012 at 07:59 PM.
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  2. #2
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    Re: Finding Minimum Surface Area

    surface area is based on a cylinder of fixed volume = 405 units cubed

    your surface area equation is missing an addition sign ...

    S = 2\pi r^2 + \frac{810}{r}

    find \frac{dS}{dr} and set the derivative equal to zero to find the value of r which minimizes S


    geometrically, graph S and locate the minimum ...


    Finding Minimum Surface Area-areamin.jpg
    Thanks from NewUser01
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  3. #3
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    Re: Finding Minimum Surface Area

    Wow, I don't know what I was thinking. That's actually quite easy to do. Thanks for the reply!
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