How fast is the area of the oil spill increasing when the radius is 30 m?

[synergix]

Homework Statement

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?

Homework Equations

A=(pi)r²

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?

 

[synergix]

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

 

[synergix]

so dA/dt = 2*30*pi

 

[Dick]

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

 

[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?

 

[Dick]

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

 

[Dick]

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?

so i am multiplying the derivative of the expression by the derivative of r?

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

 

[synergix]

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

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