Question

A ruptured oil tanker causes a circular oil slick on the surface of the ocean. When its radius is 160 meters, the radius of the slick is expanding by 0.3 meter/minute and its thickness is 0.07meter.

(a) At that moment, how fast is the area of the slick expanding? (Round your answer to three decimal places.)


(b) At that moment, the circular slick has the same thickness everywhere, and the volume of oil spilled remains fixed. How fast is the thickness of the slick decreasing? (Round your answer to seven decimal places.)

Answer 1

PART A:

The radius of the slick is increasing at a rate of (at r = 160 m)

The area of the slick is

At r = 160 m

So, the area is increasing at a rate of 5.026 m^2/s.

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PART B:

The volume of the slick is

Differentiating both the sides

Volume remains constant. So,

Putting the values

So, the thickness is decreasing with a rate of 4.375 micrometers per second.