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A container in the shape of a right circular cylinder with no top has surface area 3*pi (m2). What height h and base radius r will maximize the volume of the cylinder ?

  • math -

    surface area = πr^2 + 2πrh = 3π
    r^2 + 2rh = 3
    h = (3 - r^2)/(2r)

    V = πr^2h = (πr/2)(3-r^2)
    = (3π/2)r - (π/2)r^3

    dV/dr = 3π/2 - (3/2)πr^2
    = 0 for a max/min of V
    (3π/2)r^2 = 3π/2
    r^2 = 1
    r = ± 1, but r > 0
    r = 1

    then h = (3-1)/2 = 1

    check my arithmetic

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