If A=area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dx/dt? I'm not sure how to do this

Question

anonymous · Answer

me neither, since there is no $x$ in $A=\pi r^2$

anonymous · Answer

Related Rates

anonymous · Answer

do you mean in terms of dr/dt?

anonymous · Answer

She must mean mean dr/dt...

anonymous · Answer

oh, wow. Sorry! I meant in terms of dr/dt!

anonymous · Answer

have you heard of "related rates" before?

anonymous · Answer

Actually, you don't even need to get into that--just use the chain rule.

anonymous · Answer

You know it?

anonymous · Answer

Yes, I got 2pir(dr/dt)

anonymous · Answer

that=dA/dt

anonymous · Answer

Yeah, that's great! So what's your question?

anonymous · Answer

My actual question was "Suppose oil spills from a ruptured tanker 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?"

anonymous · Answer

Ok, now you know dr/dt = 1 m/s. And also that r=30m. So just plug those into the formula you got for dA/dt

anonymous · Answer

I got 60pim

anonymous · Answer

*m/s

anonymous · Answer

Yeah, that sounds good to me...

anonymous · Answer

Sorry, thanks so much for your help!

anonymous · Answer

No problem-- You did all the work!