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Math Help - Optimization and Finding Dimensions

  1. #1
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    Optimization and Finding Dimensions

    Another problem I'm having a tough time with.

    Find the dimensions of a box with a square bottom and no top that will hold exactly cubic inches and have the smallest possible surface area.

    The answers are apparently 1.25992A by 1.25992A by 1.25992A/2, but I have no idea how to get there. Any help would be greatly appreciated. Thanks!
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  2. #2
    MHF Contributor Unknown008's Avatar
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    The volume of the box is:

    V = lbh

    Since the bas is a square, let one side be x and the height be h, such that:

    V = x^2h

    This equals A^3;

    A^3 = x^2h

    Now, the Surface area is given by:

    S.A = x^2 + 4xh

    You have two equations now. Substitute h in the second equation and differentiate with respect to x and solve for 0, to get the value of x in those conditions (Don't forget that A^3 is a constant).

    Then, substitute the value of x to get the value of h.
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  3. #3
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    Thanks, you are the bee's knees.
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