Math

An open box , no more than 5 cm in height, is to be formed by cutting four identical squares from the corners of a sheet metal 25 cm by 32 cm, and folding up the metal to form sides.The capacity of the box must be 1575 (cm squared). What is the side length of the squares removed?

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  1. x (25 - 2x) (32 - 2x) = 1575

    expand the cubic equation

    find a solver online (use google)

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  2. size of side of square to be cut out --- x cm

    volume = (25-2x)(32-2x)(x)
    = 1575
    expanding we get:
    4x^3-114x^2 + 800x = 1575
    4x^3 - 114x^2 + 800x - 1575 = 0

    messy to solve, gave up trying to factor, and used Wolfram:
    http://www.wolframalpha.com/input/?i=solve+4x%5E3+-+114x%5E2+%2B+800x+-+1575+%3D+0

    got x = 3.5 or x = numbers outside the domain of 0 < x < 5

    the size of squares to be removed is 3.5 cm by 3.5 cm

    check:
    3.5(25-7)(32-7)
    = 1575

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  3. Thank you

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