If the radius of the tank is 20 feet and the water level fell at the rate of 4 feet per hour at 7 A.M., at what rate was water being used exactly at that time?

Question

Webster City monitors the height of the water in its cylindrical water tank with an automatic recording device. Water is constantly pumped into the tank at the rate of 2300 cubic feet per hour. If the radius of the tank is 20 feet and the water level fell at the rate of 4 feet per hour at 7 A.M., at what rate was water being used exactly at that time?

_______ cubic feet per hour

Answer 1

The decrease in volume does not depend on the height, i.e. the rate at which the height decreases is a constant because

V=πr²h=400πh and

dV/dt=400π(dh/dt)

Now just plug in the values given to get dV/dt.