Question

a ruptured oil tanker causes a circular oil slik on the surface of the ocean. when it's radius is 200meters, the radius of the slick is expanding to 0.8m/min it's thickness is 0.08 meters. at the moment, how fast is the area of the slick expanding?

Answer 1

a)

a = pir^2

da/dt = 2pirdr/dt
da/dt = 2pi*200*0.8
da/dt = 320pi m/min