calculus
posted by jon .
Gravel is being dumped from a conveyor belt at a rate of 30 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 14 feet high?

radius of cone  r
height of cone h
vol = (1/3)πr^2 h
but h = 2r or r = h/2
so
Vol = (1/3)π (h^2/4)(h)
= (1/12)π h^3
d(Vol)/dt = (1/4)π h^2 dh/dt
so when h = 14
30 = (1/12)π(196) dh/dt
solve for dh/dt