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September 20, 2014

Posted by **MILEY** on Thursday, April 8, 2010 at 2:20am.

a. How fast is the area of the slick expanding?

b. If the circular slick has the same thickness as everywhere, and the volume of oil spilled remains fixed, how fast is the thickness of the slick decreasing?

- CALCULUS -
**Damon**, Thursday, April 8, 2010 at 7:05amPretty similar to the truck and the police car:

Area = A = pi r^2

dA/dt = 2 pi r dr/dt (which by the way is the circumference times the outward speed logically enough.)

part 2 is rate of volume change

Vol = V = pi r^2 h where h is thickness

dV/dt = pi r^2 (dh/dt) + h (2 pi r dr/dt)

but

dV/dt = 0 given so

pi r^2 dh/dt = - 2 pi r h dr/dt

we did dr/dt in part 1

dh/dt = - 2(h/r)dr/dt

- CALCULUS -
**Anonymous**, Friday, October 21, 2011 at 1:33am-2.667* 10^-5

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