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Math Help - Does this equation describe the volume of the box?

  1. #1
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    Does this equation describe the volume of the box?

    A box that has a lid, "floor" that is a square with sides x, and hight is h, has a surface area of 384 dm2

    How does this equation show the volume of said box?
    V(x)=(x(192-x2))/2
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Does this equation describe the volume of the box?

    The surface area of the box in square decimeters is:

    384=2x^2+4xh and so solving for h we find:

    h=\frac{384-2x^2}{4x}=\frac{192-x^2}{2x}

    The volume is then:

    V=x^2h=x^2\left(\frac{192-x^2}{2x} \right)=\frac{x(192-x^2)}{2}
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