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
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?
1 answer