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Math Help - Calculus- volume of a square based object

  1. #1
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    Calculus- volume of a square based object

    hey guys, i am real stuck with this question and would like some help!
    The question is:
    An open top box is to be made from a square sheetof metal with a side of 12cm , by cutting a square from each corner and bending the sides up along the dashed lines.
    Find the dimensions of the cut out that will result in a box of the greatest volume.
    Sorry I dont have the drawing, but it is a square with 1 rectangle on each side.
    Thanks
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  2. #2
    MHF Contributor Amer's Avatar
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    since the sheet is square you should cut a squares from the corners not rectangles because if you cut rectangle the hight of the box will be change from side to side

    this is my answer

    let the square side be x so the volume of the box equal

    (12-2x)(12-2x)x=v
    v=4x^3-48x^2+144x
    dv/dx=12x^2+-96x+144
    0=12(x^2-8x+12)
    12(x-2)(x-6)=0
    x=2 or x=6
    substitute 2 and 6
    v(6)=0
    v(2)=128

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    Calculus- volume of a square based object-secondpic.jpg
    Last edited by Amer; May 27th 2009 at 07:43 AM.
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  3. #3
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    thanks heaps mate, really helped
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