Oil Tanker

An oil tanker aground on a reef is leaking oil that forms a circular soil slick about 0.03 m thick. It is found that the radius of the slick was increasing at 0.096 metres/minute when the radius was 150 metres. Find the rate at which the oil is leaking from the tanker.

Let the rate at which the oil is leaking be given in cubic metres per minute as dV/dt.

Now V = 0.03A where A is the area of the circular slick

and A = R² where R is the radius of the circle.

Thus	dV = 0.03 dA
          dt        dt

and	dA = 2 pi R dR
          dt          dt

so	dV = 0.03 2 pi R dR
          dt	         dt

At R= 150m,
          dR = 0.096m
          dt

So        dV = 0.03 x 2 x 3.14 x 1500 x 0.096
          dt

             = 2.71 cubic metres/min