help me please, I studies tons of times but I cannot find the answer to this question

Question

A conical water tower with vertex down has a radius of 10 ft at the top and is 22 ft high. If water flows into the tank at a rate of 28 ft3/min, how fast is the depth of the water increase when the water is 18 ft deep?

Answer 1

dV/dt = dV/dr dr/dt, so

dr/dt = dV/dt/(dV/dr)

For a cone, V =1/3πr²h

As h = 22 ft when r = 10, h = 22/10r = 11/5r

Thus, V = 1/3πr²h = 1/3πr²*11/5r = 11/15πr³

dV/dr = 3 * 11/15πr² = 11/5πr²

When h =18 ft, r = 5/11 * 18 = 90/11 ft

dV/dr = 11/5π(90/11)² = 1620/11π ft²

dr/dt = dV/dt/dV/dr = 28 ft³/min/(1620/11π ft²) = 77/(405π) ft = .060518 ft