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A box has rectangular sides, top and bottom. The volume of the box is 3 cubic meters. The height of the box is half the width of the base. Express the total surface area of the box in terms of the height of the box.

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  1. If the height is h, then the base has dimensions 2h and y, so

    2h^2y = 3
    so y = 3/(2h^2)

    and the area is two pairs of vertical faces:

    2(2h*h + y*h) = 2(2h^2+3/(2h^2)*h)
    = 4h^2 + 3/h

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