Calculus

If an open box has a square base and a volume of 106 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction. (Round your answers to two decimal places.)
height in
length in
width in

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  1. V = L*W*H = 106in^3,

    Since the base is square,
    W = H.
    L*W*W = 106,
    L*W^2 = 106,
    To minimize the material,
    let L = W:
    W*W*W = 106,
    W^3 = 106,
    W = crt(106) = 4.73in.
    L = 4.73in.
    H = 4.73in.

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