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 whose base diameter and height are always equal to each other. How fast is the height of the pile increasing when the pile is 20 feet high?

Answer 1

v=1/3*pi*r^2h r=2/h
V=1/3*pi*(h/2)^2*h
=1/3*pi*h^2/4*h
=1/12*pi*h^3

V'=10ft^3/min
h=20ft

V'=1/12*pi*3h^2*h'

10=1/12*pi*3(20)^2*h'
solve for h'