Gravel is being dumped from a conveyor belt at a rate of 15 ft^3/hr and its courseness is such that is forms a pile in the shape of an inverted right cone whose height is three times its base radius. How fast is the height of the pile increasing when the pile has a height of 10 feet?

Answer 1

h=3r, so r = h/3

v = π/3 r^2 h = π/3 (h/3)^2 h = π/27 h^3

dv/dt = π/9 h^2 dh/dt

So, plug in your numbers to get dh/dt.