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22 December, 20:24

An open box with a volume of 1500 cm cube is to be constructed by taking a piece of cardboard 20 cm by 40 cm, cutting squares of side length x cm from each corner, and folding up the sides. Find the exact dimensions of the box.

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  1. 22 December, 20:49
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    The dimensions of the box formed will be:

    width: 20 - 2x

    length: 40 - 2x

    height: x

    Volume = width x length x height

    1500 = x (20 - 2x) (40 - 2x)

    1500 = x (800 + 4x² - 120x)

    1500 = 4x³ - 120x² + 800x

    0 = 4x³ - 120x² + 800x - 1500

    0 = x³ - 30x² + 200x - 375

    Solving the cubic equation:

    x = 5 (only integer root)

    Length = 30 cm

    Width = 10 cm

    Height = 5 cm
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