Math basic related rates please help? ?

Question

An oil spill is growing in a circular shape. The radius is increasing at the rate of 5 miles per day. How fast is the area changing when the circumference is at 49 Π ?

i know this has to do with derivatives, and any help is appreciated.

Answer 1

Thus dr/dt =5mi/day; Area is A=pi*r^2, hence

dA/dt = 2pi*r*dr/dt, where 2pi*r =49*pi is circumference;

thus dA/dt = 49*pi*5 = 245*pi mile^2/day;