Am I doing this related rates right?

[TheFallen018]

Hey guys,

I have this related rates problem that I'm working through. I think I might have an answer, but I'm not sure.

Here's the question.
A potter shapes a lump of clay into a cylinder using a pottery wheel.
As it spins, it becomes taller and thinner, so the height, h, is increas-
ing and the radius, r, is decreasing. If the height of the cylinder is
increasing at 0.1 cm per second, find the rate at which the radius is
changing when the radius is 1.5cm and the length is 7cm.

I used the volume of the cylinder for this, and attempted to differentiate it. I ended up with this:

$\frac{d}{dt}V=\frac{d}{dt}(\pi{r}^{2}(t)h(t))$

$0=\pi(2r\frac{dr}{dt}h+\frac{dh}{dt}{r}^{2})$

Which broke down to:

$\frac{dr}{dt}=-\frac{h'{r}^{2}}{2rh}$

Which came out as approximately -0.0107 cm/sec

Does this look about right, or have I gone horribly wrong?

Thanks :)

 

[joypav]

Looks good. I got the same answer.

 

[HOI]

I feel an overwhelming need to point out that \frac{-h'r^2}{2rh}= \frac{-h'r}{2h}.