Water is flowing into a hemispherical bowl of radius 5 feet at a constant rate of 1 cubic foot per minute.
(a) At what rate is the top surface of the water rising when its height above the bottom of the bowl is 3 feet? 4 feet? 5 feet?
(b) If h(t) is the depth in feet at time t, find the second derivative of h when h=3, h=4, and h=5.