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Math. HELP!

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A cylinder is to be made of circular cross-section with a specified volume. Prove that if the surface area is to be a minimum, then the height of the cylinder must be equal to the diameter of the cross-section of the cylinder.
Maybe it's the wording, but I have not been able to crack this one for the past half-hour!

  • Math. HELP! - ,

    let the radius be r and the height be h
    let the volume be V, where V is a constant
    πr^2h = V
    h = V/(πr^2)

    Area = 2 circles + rectangle
    = 2πr^2 +2πrh
    = 2πr^2 + 2πr(V/πr^2)
    = 2πr^2 + 2V/r
    d(Area)/dr = 4πr - 2V/r^2
    = 0 for a max/min of area
    4πr = 2V/r^2
    r^3 = V/(2π) = πr^2h/2π
    r = h/2
    or
    2r = h
    diameter = height !!!!

  • Math. HELP! - ,

    Reiny. You. Are. God. Thank you :D

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