# Differentials and Rates of Change; Related Rates

1. Oct 23, 2013

### Qube

1. The problem statement, all variables and given/known data

2. Relevant equations

Product rule; implicit differentiation.

Volume of cylinder, V = pi(r^2)(h)

3. The attempt at a solution

dV/dt = 0 = pi[2r(dr/dt)(h) + (dh/dt)(r^2)]

Solve the equation after plugging in r = 5; h = 8, and dh/dt = -2/5. Solve for dr/dt.

0 = 80pi(dr/dt) - 10pi

1 = 8(dr/dt)

dr/dt = 1/8

Last edited by a moderator: May 6, 2017
2. Oct 23, 2013

### elvishatcher

You are not trying to find $\frac{dr}{dt}$. Each part of the question wants you to find $\frac{dV}{dt}$ for a given rate at which the radius is changing (think about what represents the rate of change of the radius).

3. Oct 23, 2013

### iRaid

It says to find the rate of change of the radius in the first part of the question.

I think you just have to have it like this: $\frac{dV}{dt}=2\pi r\frac{dr}{dt}\frac{dh}{dt}$, then just plug in values.

Edit: Oh forgot to add, the V is constant, so what does that mean the value of dV/dt is?

Last edited: Oct 23, 2013
4. Oct 23, 2013

### haruspex

It's multiple choice. V is given as constant, dh/dt is a given value, so the obvious approach is to calculate dr/dt and see which choice matches. Of course, you could run it the other way: for each choice compute dV/dt and see which one gives 0, but that probably takes longer on average.
You mean V is constant, so what value is dV/dt, right?

5. Oct 23, 2013

### iRaid

Yes, my mistake.

6. Oct 27, 2013

### Qube

Is 1/8 the correct answer? I've redone the work again below:

7. Oct 27, 2013

### Qube

8. Oct 27, 2013

Yes.