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?