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 to each other. How fast is the height of the pile increasing when the pile is 23 feet high?

Answer 1

volume of cone = (1/3)pi(r^2)h
but h=2r
or r = h/2
then volume = (1/12)pi(h^3)
dV/dt = (1/4)pi (h^2) dh/dt

20 = (1/4)pi (23^2)dh/dt
etc