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

As we knw that the dr/dt = 2
 And  The area of the circular slick is given by formul
 A = (pi)r^2.
Now lets take derivative: dA/dt=2πrdr/dt
As we knw that radius is 25
sodA/dt=2π(25)(2)=100π
which is equal to
=314.16 per minute this is how area is increasing
now for part b
 t = 4, the radius will have increased to 8 m.
   now we will put the values in formula dr/dt
so it will be.dA/dt=2π(8)(2)
=32π
=100.53 is the answer
hope it helps

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