1. ## Rates of Change

So, the question is this:
Suppose oil spilled from a tanker spreads in a circle whose area increases at a constant rate of 6 square miles per hour. How fast is the radius of the spill increasing when the area is 9 square miles?

Now, I think dA/dt= 6 square miles. I'm not as sure about the 9, because if you take the derivative there is no A it's just dA/dt= pi*2r*dr/dt. So, if I solve for dr/dt then won't I still have the 2r left?

Help would be much appreciated with this, thanks.

2. Originally Posted by instantchaos
So, the question is this:
Suppose oil spilled from a tanker spreads in a circle whose area increases at a constant rate of 6 square miles per hour. How fast is the radius of the spill increasing when the area is 9 square miles?

Now, I think dA/dt= 6 square miles. I'm not as sure about the 9, because if you take the derivative there is no A it's just dA/dt= pi*2r*dr/dt. So, if I solve for dr/dt then won't I still have the 2r left?

Help would be much appreciated with this, thanks.
You will but this is where the 9 comes into play via the equation

$A=\pi r^2$ so Since you know $A$ you can solve for $r$.