Solving for Rate of Change in Sand Pile Height

[lax1113]

Homework Statement

Sand is falling into a conical pile at a rate of 10 cubic feet/minute. The diameter of the cone is 3 times the altitude. At what rate is the height of the pile change when the height=15feet.


So i was going through and I don't know if i derived it wrong, but i had

v=1/3pi(r^2)h

so

dv/dt= pi/3 R^{2}(dh/dt) * 2pi/3 R (h)

but when i go through and solve it all with R= 3/2h I don't get the answer form the back of the book. Is my derivative wrong? I used chain rule...

 

[Dick]

V(t)=(1/3)pi(r(t)^2)*h(t). If you do the derivative correctly, there ought to be a dr(t)/dt hanging around someplace. And why is there a '*' between the two parts of what looks like a product rule?