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Math Help - Minimum surface area problem

  1. #1
    Member
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    Oct 2007
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    Minimum surface area problem

    A closed rectangular box has a volume of 32 cm^3. What are the lengths of the edges giving a minimum surface area?

    I came up with an equation for surface area:

    2(32/xy) + 2(32/x) + 2(32/y) with x and y being the length and width of the edges and height solved in terms of x and y so I just have two variables.

    Next, I got my f sub x and f sub y and set them equal to zero to obtain a global min. I must be doing something crazy because I keep getting only a negative value for x which is equal to y at -1 which is wrong. The answer is 32^(1/3) but I sure can not get this. Any help on where I went wrong would be much appreciated. Frostking
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  2. #2
    Member
    Joined
    Jan 2009
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    I think you are computing the height wrongly:

    2(32/xy) + 2(32/x) + 2(32/y) SHOULD BE

    2(xy) + 2(32/x) + 2(32/y)

    Please try again.

    -O
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