(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Before anybody tells me to check the web for this problem, I have and this is very different from what is out there.

An oil spill spreads in a circular pattern. Suppose the area is increasing at a rate of 800 square feet for every 1 foot increase in its radius (which is increasing at a rate of 15 feet per hour.) What is the rate of change of the area of the spill with respect to time?

2. Relevant equations

3. The attempt at a solution

So I am looking for somebody to explain why my answer is wrong and the professors is right (and nobody needs to say because he's the professor). I asked and he couldn't explain this clearly and I am very curious. This was on our last test.

My attempt:

A=πr^2

A'=2πr

dr/dt=15 da/dr=800 find da/dt

da/dt=2*π*800*15

=24000π ft^2/hr

His answer:

da/dt=800*15

=12000 ft^2/hr

Why is his right and where is the 2π?

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# Help check a related rate problem

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