2019 AP Calculus AB FRQ #4

A cylindrical barrel with a diameter of 2 feet contains collected rainwater, as shown in the figure above. The water drains out through a valve (not shown) at the bottom of the barrel. The rate of change of the height h of the water in the barrel with respect to time t is modeled by dh/dt = -1/10 * h ^1/2, where h is measured in feet and t is measured in seconds. (The volume V of a cylinder with radius r and height h is V = pr 2 h.)
(a) Find the rate of change of the volume of water in the barrel with respect to time when the height of the water is 4 feet. Indicate units of measure.
(b) When the height of the water is 3 feet, is the rate of change of the height of the water with respect to time increasing or decreasing? Explain your reasoning.
(c) At time t = 0 seconds, the height of the water is 5 feet. Use separation of variables to find an expression for h in terms of t.
Timestamps
Intro: 00:00
Part a: 00:35
Part b: 02:53
Part c: 05:30

[@shinedownracing425]

Thanks! I couldn’t figure out what I was supposed to do with dr/dt