Related Rates Question?

Question

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone, such that the ration of the base diameter to the height is always equal to 1. How fast is the height of thepile increasing when the pile is 17 feet high?

Can someone explain how to do this problem??

thanks

Answer 1

volume=(1/3)pir^2h
=(1/3)pi(d^2/4)h
=(1/3)pi(h^2/4)*h
=(1/12)pih^3
dV/dh=(1/12)3*h^2*(dh/dt)
10=(1/4)(17^2)(dh/dt)
dh/dt=40/289 ft/min
=approx 0.14 '/min

Answer 2

d == h = 2r
V = (1/3)πr^2h
V = (1/3)π(h/2)^2h
V = (1/12)πh^3
dV/dt = (dV/dh)(dh/dt) = (3/12)πh^2(dh/dt) = 10 ft^3/min
dh/dt = (10 ft^3/min)/((3/12)πh^2)
dh/dt = (40 ft^3/min)/(π17^2)
dh/dt = (40 ft^3/min)/(π289) ft/min
dh/dt = 0.0440576 ft/min