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Math Help - Math 120 pizza box problem3

  1. #1
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    Math 120 pizza box problem3

    Pagliacci Pizza has designed a cardboard delivery box from a single piece of cardboard, as pictured.

    (a) Find a polynomial function v(x)
    that computes the volume of the box in terms of x.
    (b) Find a polynomial function a(x)
    that computes the exposed surface area of the closed box in terms of x.
    (c) What are the explicit dimensions if the exposed surface area of the closed box is 600 sq. inches? (Round your dimensions to three decimal places. Enter your answers as a comma-separated list.)

    For (a) I got, incorrectly, v(x)=2x3-120x2+500x = x3-60x+250 because, I thought, L(W)(H)
    length = 20-2x
    height = x
    width = (50-2x)/2

    For (b) I am at a complete loss.
    I would guess:
    length= 2(20-2x)
    width= 2(25-2x)
    height=x

    plug into:
    surface area of a box: 2lw + 2lh + 2wh
    ???

    therefore for (c) I do not know what to set equal to 600

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  2. #2
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    Re: Math 120 pizza box problem3

    This is a nice little problem.

    $x(25 - x)(20 - 2x) = x(500 - 70x + 2x^2) = 2x^3 - 70x^2 + 500x \ne 2x^3 - 120x^2 + 500x.$

    You got the conceptual part right and then messed up the algebra.

    For part b, why would the dimensions be different for that part than for a?
    Thanks from HallsofIvy and UWstudent
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