Calc

You want to make a rectangular box, open at the top, by cutting the same size square corners out of a rectangular sheet of cardboard and then folding up the sides. The cardboard measures 10 in. by 12 in. What are the dimensions of the box that will have greatest volume if the possible corner cuts measure 1 in., 2 in., 3 in., or 4 in.?

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asked by kaa

  1. well, the volume is width * length * height (x)

    v = (10-2x)(12-2x)(x)
    now plug in x=1,2,3,4 and see which gives the greatest volume

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    posted by Steve

  2. a.9 in. by 12 in. by 1 in.
    b.3 in. by 6 in. by 4 in.
    c.7 in. by 10 in. by 2 in.
    d.5 in. by 8 in. by 3 in.

    c?

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    posted by kaa

  3. Nope. Think about it. Since the two original dimensions are 8x10, after the cuts, the base of the box will be

    8x10
    6x8
    4x6
    2x4

    You cannot even get (c) by cutting equal squares from all corners.

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    posted by Steve

  4. is it a?

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    posted by nene

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