Math

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From an 8 inch by 10 inch rectangular sheet of paper, squares of equal size will be cut from each corner. The flaps will then be folded up to form an open-topped box. Find the maximum possible volume of the box.

  • Math -

    x is size of side of square cut out
    then height of box x
    length = (10-2x)
    width =(8-2x)
    V = x (10-2x)(8-2x)
    V = x(80 - 36x + 4x^2)
    V = 80 x - 36 x^2 + 4 x^3
    dV/dx = 80 -72 x + 12 x^2
    dV/dx = 0 for max or min
    so
    3x^2 - 18x + 20 = 0
    (3x-5)(x-4) = 0
    x = 5/3 or x = 4
    x = 4 gives zero volume
    so I suspect x = 5/3

  • Math -

    Damon's answer is almost right, but you have to use the quadratic equation x is 5.055... and 1.472... so basically 1.472. The volume is then about 13.583in^3

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