calculus

An open-topped cylindrical pot is to have volume 125 cm3. Determine the minimum possible amount of material used in making this pot? Neglect the thickness of the material as well as possible wastage. Give your answer accurate to 2 decimal places

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  1. In other words determine the minimum surface area for the given volume.

    V = pi r^2 h
    so h = 125/(pi r^2)

    A = pi r^2 + 2 pi r h

    A = pi r^2 + 2 pi r(125/(pi r^2))
    A= pi r^2 + 250/r
    dA/dr = 0 at min = 2 pi r -250/r^2

    so
    2 pi r = 250/r^2
    pi r^3 =125
    pi^(1/3) r = 5
    r = 5/pi^(1/3)

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