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Consider a right circular cylinder whose total surface area (top, bottom, side) is 300 pi; what must its radius be in order that the volume be as large as possible

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    2πr^2 + 2πrh = 300
    h = (300-2πr^2)/2πr
    = 150/πr - r

    v = πr^2 h = πr^2(150/πr - r)
    = 150r - πr^3

    dv/dr = 150-3πr^2
    max v occurs when r=√(50/π)

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