Question: Concentric circles are formed when a stone is dropped in a pool of water.
a) What is the average rate of change in the area of one circle with respect to the radius as the radius grows from 10 cm to 50 cm?
b) How fast is the area changing with respect to the radius when the radius is 75 cm?
*I solved for part a) by using the area of a circle formula ($A(r) = πr^2$) to find AROC. The result that I got was 188.4 or 60π.
However, as I get to part b), I get confused of what the question is asking me. The question is asking what the speed is. I did try to do this question on my own by grabbing the equation and inserting the r value for 75 and solving for the Area. But that's not what the question is asking for right? It's asking for the speed. So how would I solve for part b.)?
I'd appreciate if anyone can help me out.
Part a) $$ AROC=\frac{A(50)-A(10)}{50-10}= 60 \pi \;cm $$ Part b) $$ A'(r)=2\pi r \\A'(75)=2\pi (75) = 150\pi \; cm $$