(2) A box with an open top is to be constructed from a rectangular piece of cardboard by cutting out equal squares of side x at each corner and then folding up the sides. If the dimensions of the cardboard are 12 by 20, express the volume V of the box as a function of x.
SOLUTION:
Volume = length x width x height = (20 - 2x)(12 - 2x)x = 4x3 - 64x2 + 240x The volume in terms of the height of the box is given by 4x3 - 64x2 + 240x.