calculus

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Find the formula for the described function and state its domain. An open rectangular box with a volume of 8 cubic meters has a square base. Express the surface area of the box as a function of S(x) of the length x of a side of the base.

  • calculus -

    from the volume,
    8 = x * x * h
    h = 8/(x^2)
    therefore,
    surface area = 2lw + 2lh + 2wh
    where l=length, w=width, h=height
    since it's an open box:
    S(x) = x^2 + 2[8/(x^2)](x) + 2[8/(x^2)](x)
    S(x) = x^2 + 32/x

    so there,, :)

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