Gravel is being dumped from a conveyor belt at a rate of 15 ft^3/hr and its coarseness 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

height ------- h
base radius --- h/3

V = (1/3)π r^2 h
= (1/3)π (h^2/9)(h) = (π/27) h^3

dV/dt = (π/9) h^2 dh/dt
for the given data:
15 = π/9 (100)dh/dt
dh/dt = 135/(100π) ft/hr