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Math Help - Can someone please show me how to do this?

  1. #1
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    Can someone please show me how to do this?

    An open box with a square base is constructed from a square piece of cardboard 24 inches on a side by cutting out a square from each corner of the cardboard and turning up the sides. express the volume V as a function of the length x of the side of the square cut from each corner.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by wayneo1688 View Post
    An open box with a square base is constructed from a square piece of cardboard 24 inches on a side by cutting out a square from each corner of the cardboard and turning up the sides. express the volume V as a function of the length x of the side of the square cut from each corner.
    You know that each square has a side of length x. So two of those are taken from each side of the cardboard, right? Thus when the side pieces are folded up the remaining base is a square with sides of length 24 - 2x.

    I'll leave it to you to figure out the height of the box and the volume.

    -Dan
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  3. #3
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    Express volume

    thanks, but how do i express the volume as a function of the length x of the side of the square cut from each corner?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by wayneo1688 View Post
    thanks, but how do i express the volume as a function of the length x of the side of the square cut from each corner?
    The volume of a rectangular solid is given by
    V = lwh
    where l is the length of the base, w is the width of the base, and h is the height of the solid.

    You have a square base, so l = w = 24 - 2x. When you fold the corners up (each having a length of x) what height does that give you for the box? (If you can't see this immediately you are over-thinking the problem. It's obvious.)

    -Dan
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