# Homework Help: DA/dt of expanding circle

1. Oct 24, 2009

### synergix

1. The problem statement, all variables and given/known data
a) if A is the area of circle with radius r and the circle expands as time passes, find dV/dt in terms of dr/dt
b)Suppose oil spills from a ruptured ranker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 30 m?

2. Relevant equations

A=(pi)r2

3. The attempt at a solution

dA/dt= ((pi)r2)'=(r2+2(pi)r)

dA/dt= ((pi)2(30) + 302)

is this correct? it seems like an awfully big number what have I done wrong?

2. Oct 24, 2009

### synergix

oh wait I am treating pi like a variable not a constant. durh

3. Oct 24, 2009

### synergix

so dA/dt = 2*30*pi

4. Oct 24, 2009

### Dick

You've got it dA/dt=pi*2*r*dr/dt.

5. Oct 24, 2009

### synergix

OK so I would need to have multiplied 2*pi*r*1m/s but since its one it doesn't matter but that is what is happening correct?

I am multiplying the derivative of the expression by the derivative of r?

6. Oct 24, 2009

### Dick

It matters if you are keeping track of units. That's where the m/s came from.

7. Oct 24, 2009

### Dick

You are using the chain rule. d/dt(f(r))=d/dr(f(r))*dr/dt. You knew that, right?

8. Oct 24, 2009

### synergix

I know that now. I missed a good couple classes (long story short) because I had no other choice. Now I am trying to catchup. I guess I better do some reading..thanks