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Math Help - Find a Function

  1. #1
    MHF Contributor
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    Find a Function

    United States Service has contracted you to design a closed box with a square base that has a volume of 5000 cubic inches. Find a function for a surface area of the box.

    Given Data:

    height of box = y

    width of box = x

    length of box = x
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  2. #2
    Super Member Matt Westwood's Avatar
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    Surface area is:

    Area of bottom + area of top + area of all 4 sides.

    As the base is square, the areas of the top and bottom are both x^2.

    The area of each side is xy.

    So the total surface area is 2x^2 + 4xy = 2x (x + 2y).

    Now we can work out what the side y is in terms of x, because we know that the volume is 5000.

    So we know that x times x times y = 5000, or that y = 5000/(x^2).

    So we can plug this expression for y into the one for surface area:

    Surface area = 2x (x + 2 (5000/(x^2))


    A reasonable question to ask next is to find the value of x which makes the surface area a minimum - but only if you've done calculus.
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  3. #3
    MHF Contributor
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    Nicely done!

    Another great reply. I am learning so much on this website.

    Great job guys!
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