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March 24, 2017

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a sheet of cardboard is to be folded up to make a closed box. If the cardboard measures 55 cm by 80cm calculate the maximum volume of the box that can be made from this sheet of cardboard

  • Maths- Calculus - ,

    let each side of the squares to be cut out be x cm
    length = 80-2x
    width = 55-2x , 0 < x < 27.5
    height = x

    V = x(80-2x)(55-2x)
    = 4x^3 -270x^2 + 4400x

    dV/dx = 12x^2 - 540x + 4400
    = 0 for a max of V

    3x^2 - 135x + 1100 = 0
    x = (135 ± √5025)/6

    take it from there (I get x = appr 10.69)

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