calculus

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An oil can is to be made in the form of a right circular cylinder to have a volume of 16 pie inches cubed. Find the dimensions of the can that requires the least amount of material

  • calculus -

    v = pi r^2 h
    a = 2 pi r^2 + 2 pi r h

    h = 16pi/pi r^2 = 16/r^2

    a = 2 pi r^2 + 2 pi r 16/r^2
    = 2pi (r^2 + 16/r)

    min area when 2r - 16/r^2 = 0

    2r^3 - 16 = 0
    r = 2

    So, the can has a radius of 2 and a height of 4

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