I need help with this cal 1 related rates question?

Gravel is being dumped from a conveyor belt at a rate of 20 ft^3/min. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 19 ft high?

1 Answer
Nov 11, 2016

80/(19^2pi)80192π ft/min

Explanation:

We know d=h, =>r=h/2d=h,r=h2

So V=1/3pi(h/2)^2h\ \ \ =>\ \ \ V(t)=pi/12h^3(t)

Differentiating over t

V'(t)=pi/4h^2(t)h'(t)

We know V'(t)=20 \ \ AA t\ \ ,\ \ \ h(t_0)=19
So

20=pi/4*19^2h'(t_0)

h'(t_0)=80/(19^2pi)