A box is to be made out of a 10 cm by 14 cm piece of cardboard. Squares of side length 9: cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. (a) Express the volume V of the box as a function of an. V = 4x3 48x2 + 140x cm3 (b) Give the domain of V in interval notation. (Use the fact that length, width and volume must be positive.) (c) Find the length L, width W, and height H of the resulting box that maximizes the volume. (Assume that W S L). W.-... H = 1.918 cm (d) The maximum volume of the box is 120.16 cm3