The radius of a circular oil slick expands at a rate of 2 m/min.

(a) how fast is the area of the oil slick increasing when the radius is 25 m
(b) if the radius is 0 at time , how fast is the area increasing after 4 mins

Well part A gives us the radius of 25M so we have enough to find how fast the area is changing.
We will use the equation > dA/dt = 2pirdr/dt 
dA/dt = 2pi(25)(2) = 100pi = 314.6
So the area would be increasing by 314.6 square meters per minute or 100pi square meters per minute.
For part B we have t = 0  which then means t = 4, the value will then have increased to 8m. So we plug it into the equation.
dA/dt = 2pi(8)(2) = 32pi = 100.53
This means the area is increasing at 100.53 square meters per minute at t = 4!

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