Related Rats Problem: Conical Sand Pile...

[jessi88]

Sand falls from a conveyor belt at a rate of 10 m^3/min onto the top of a conical pile. The height of the pile is always three-eighths of the base diameter. How fast are the a) the height and b) the radius changing when the pile is 4 m high?

Volume of a cone is V = 1/3 pi r^2h

Thus, I found that h = 3r/4 or r = 4h/3

I was wondering how to solve for the rate of change for the height (dh/dt) and the rate of change of the radius (dr/dt) when the pile is 4 m high

Thank you

 

[galactus]

You're on the way.

\(\displaystyle V=\frac{1}{3}{\pi}r^{2}h\)

\(\displaystyle V=\frac{1}{3}{\pi}(\frac{4}{3}h)^{2}h\)

\(\displaystyle V=\frac{16{\pi}}{27}h^{3}\)

Now, do that differentiation thing and solve for dh/dt.