You have to make a square-bottomed, unlidded box with a height of three inches and a volume of approximately 42 cubic inches. You will be taking a piece of cardboard, cutting three-inch squares from each corner, scoring between the corners, and folding up the edges. What should be the dimensions of the cardboard to the smartest quarter inch?

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  1. since the bottom is square, you will be using a square piece of cardboard.

    So, if the uncut piece is of side x. after the cut, you will have volume

    v = (x-6)^2 * 3

    Now, you want v=42, so solve

    3(x-6)^2 = 42
    (x-6)^2 = 14
    x = 6+√14

    so, after cutting and folding, the volume will be √14*√14*3 = 42

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