Related rates .. calculus .. help?

Question

Wheat is poured through a chute at the rate of 10 ft^3/min and falls in a conical pile whose bottom radius is always half the altitude. How fast will the circumference of the base be increasing when the pile is 8 ft high?
I know that v= (1/3) py r^2 h
because r equals half h so
v= (2/3) py r^3
differentiate: (dv/dt) = 2py (r^2) (dr/dt)
and we also know that the circumference:
(dc/dt) = 2 py (dr/dt)
and then what can I do ??
plz help

Answer 1

dv/dt is a fixed number, namely 10.

From that you know dr/dt whenever you know h (and hence r).

And when you know dr/dt and r, you know dc/dt.

You're basically done -- just plug in the specific numbers!