An open-top box is to be formed by cutting congruent squares from the four corners of a 20 cm by 30 cm rectangular sheet of cardboard and folding up the flaps.
Let x centimeters be the side length of each square to be removed.
(a) Write a formula V(x) for the volume of the box as a function of x.
(b) Determine the value of x that maximizes V(x), justifying that this value indeed yields a maximum.
(c) Compute the maximum volume of the box to the nearest whole cubic centimeter and interpret this value in context.