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Math Help - Maximise surface area of cuboid given constant volume.

  1. #1
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    Maximise surface area of cuboid given constant volume.

    Hopefully this is the right section to be putting this ...
    A cuboid tank is open at the top and the internal dimensions of its base are x m and 2x m. The height is h m. The volume of the tank is V cubic metres and the volume is fixed. Let S m^2 denote the internal surface area of the tank.
    Find S in terms of x and h; and V and x.
    State the maximal domain for the function defined by the rule in the above question.
    If 2 < x < 15 find the maximum value of S if V=1000m^3.
    Thank you.
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    Quote Originally Posted by mandarep View Post
    Hopefully this is the right section to be putting this ...
    A cuboid tank is open at the top and the internal dimensions of its base are x m and 2x m. The height is h m. The volume of the tank is V cubic metres and the volume is fixed. Let S m^2 denote the internal surface area of the tank.
    Find S in terms of x and h; and V and x.
    State the maximal domain for the function defined by the rule in the above question.
    If 2 < x < 15 find the maximum value of S if V=1000m^3.
    Thank you.
    Surely you are familiar enough with the formulae for the volume and surface area of a cuboid to answer the first part ....? (And you can therefore get h in terms of V and x and so substitute into S)

    Please show some effort here and say where you're stuck.
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