Gravel is being dumped from a conveyor belt at a rate of 20 {\rm ft}^3{\rm /min}. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 18 ft high?

Answer 1

v = 1/3 πr^2 h = π/3 (d/2)^2 h = π/12 h^3

dv/dt = π/4 h^2 dh/dt

Now just plug in your numbers.

Answer 2

1526.81403