Had an epiphany. You do have to use derivatives, and it is quite simple if you know how.

Area of Cone: (1/3)*(pi)*(r)^3

Take the derivative with respect to time:
dAC/dt = (pi)*(r)^2*(dr/dt)

Look at what is known:
dAC/dt is 10 cu ft.
r is cubed root of (3000/pi) as previously found.

Solve for (dr/dt) which is the change in radius with respect to time.
dr/dt = .0328248340614
There's your answer.

What is it they say about silence being golden?