Barrons AP Calculus - David Bock

11. (a) Let h represent the depth of the water, as shown.

Then h is the altitude of an equilateral triangle, and the base

The volume of water is

Now and it is given that Thus, when h = 4,

(b) Let x represent the length of one of the sides, as shown.

The bases of the trapezoid are 24 − 2x and 24 − 2x + and the height is

The volume of the trough (in in.^3 ) is given by

Since the maximum volume is attained by folding the metal 8 inches from tne

edges.