Related Rates and an Oil Slick

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SUMMARY

The discussion centers on the mathematical analysis of a circular oil slick caused by a ruptured tanker. When the radius of the slick reaches 150 meters, it expands at a rate of 0.1 meters per minute, with a constant thickness of 0.02 meters. The participants clarify that the area in question refers specifically to the surface area of the circular top of the slick, not the entire cylindrical volume. The calculations for both the rate of area expansion and the rate of thickness decrease are confirmed to be straightforward once the correct interpretation is established.

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A ruptured oil tanker causes a circular oil slick on the surface of the ocean. When its radius is 150 meters, the radius of the slick is expanding by 0.1 meter/minute and its thickness is 0.02 meter. At that moment:

(a) How fast is the area of the slick expanding?
(b) 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?

Part B is easy, I just used a cylinder and figured it out. I'm sure I got it correct.

Part A is where I'm confused. When they say area, I wonder do they mean just the surface area of the top of the slick (a circle), or the surface area of the entire cylinder?

What do you people think?
 
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I think they mean just the surface area of the top of the slick.
 

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