# Related Rates Question

1. Jan 22, 2006

### Jordan_

I've been working on this problem for a while now and I can't seem to make it work. Maybe I could get a hint?

I understand I'm given dv/dt = 180 as well as r = 6 and h = 2r/5 = 36/5

The equation I'm using is v = Bh/3 or v = (pi)(r^2)(h)/3

I go on to take the derivative and input my variables but I'm always missing dr/dt. Maybe a hint?

By the by the answer is stated as 1.59m/h

2. Jan 22, 2006

### StatusX

You want an equation relating the volume of the pile to its height, which you can get by writing the radius in terms of the height. Then take the derivative of both sides.

3. Jan 22, 2006

### Jordan_

Okay so if my volume equation is

v = pi(r^2)(h) and I want to get rid of the radius, I simple take the information I was given...that the heigh is one fifth the diameter of the circle and for the equation h = 2r/5. I then rearrange it to say r = 5h/2 and substitute that in?

Then it makes v = pi(5h/2)^2(h) which then gives me v = pi(25h^3)/4

when I take the derivative of that, and sub in the height which I get as 2.4,
I end up with dh/dt = 1.27m which isn't the right answer. What am I doing wrong?

4. Jan 22, 2006

### StatusX

Well, the volume should be $\pi r^2 h/3$, but that mistake would give you an answer that's off by a factor of three, so you must be making another error in some calculation you haven't shown.

5. Jan 22, 2006

### Jordan_

Sorry about that mate. Least I could have done is checked over my calculations before asking. I just did it again your way and got the answer. Thanks for the help bro it's appreciated.