The length l, width w, and height h of a box change with time. At a certain instant the dimensions are l = 1 m and w = h = 2 m, and l and w are increasing at a rate of 2 m/s while h is decreasing at a rate of 3 m/s. At that instant find the rates at which the following quantities are changing.
(a) The volume
(b) The surface area
(c) The length of a diagonal