# Related Rates Clay Pot Problem

1. Nov 5, 2013

### Burjam

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

A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder increases and the radius, r decreases. If the length 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 cm and the length is 5 cm.

2. Relevant equations

N/A

3. The attempt at a solution

So I know that dL/ds=0.1. But I don't know exactly how the radius changes as L changes. I'm having trouble setting up a function for this. If I had that I could do the rest of the problem.

2. Nov 5, 2013

### Dick

The volume is constant as the potter rolls. What's an equation for the volume of a cylinder in terms of the radius and length?

3. Nov 5, 2013

### Burjam

V=Lπr2

But how can I connect this with time?

4. Nov 5, 2013

### Dick

Differentiate both sides d/dt.

5. Nov 5, 2013

### Burjam

How can I differentiate this function with respect to time?

6. Nov 5, 2013

### Dick

V is a constant. r and L are both functions of time. Write V=πr(t)^2*L(t). Now differentiate it.

7. Nov 5, 2013

### Burjam

Thank you I think I figured it out:

dV/dt=2L(t)πr(t)r'(t)+L'(t)πr(t)2
0=2L(t)πr(t)r'(t)+L'(t)πr(t)2
0=2L(t)r'(t)+L'(t)r(t)
2L(t)r'(t)=-L'(t)r(t)
r'(t)=-L'(t)r(t)/2L(t)r'(t)
r'(t)=-0.1(1)/2(5)
r'(t)=-0.1/10=-0.01cm/s

8. Nov 6, 2013

### Dick

Right. Well done.