q-5 How would I solve this?

Question

Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 12 feet high?

Recall that the volume of a right circular cone with height h and radius of the base r is given by 

Answer 1

V = πr²h/3

diameter, d = h = 2r --> r=h/2

V=πh³/12

dV/dt = πh²/4 dh/dt= 20

dh/dt = 80/(πh²)

When h = 12 ft

dh/dt = 80/(π144) = 5/(9π) ft³/min