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Math

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You are in charge of a tank to be used for water storage. Your boss has told you that he wants a cylindrical tank with a minimum capacity of 300,000 cubic feet. Your boss wants to spend the least possible amount in painting the tank. Design a tank to meet this objective.

  • Math - ,

    Let y be the height. The diameter D must satisfy
    (pi/4) D^2 y = 3*10^5 ft^3

    The area to be painted (including the top) is
    A = pi [D^2/4 + D y]
    Substitute using the first equation to eliminate y.
    A = pi [D^2/4 + 3*10^5 (4/pi)(1/D)]

    Set dA/dD = 0 and solve for D

    D/2 - (12*10^5/pi)/D^2 = 0
    D^3 = 24*10^5/pi
    D = 92.6 ft

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