Sunday

March 29, 2015

March 29, 2015

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

**Answer this Question**

**Related Questions**

math please help - A ruptured oil tanker causes a circular oil slick on the ...

MATH-CALC - 3.A ruptured oil tanker causes a circular oil slick on the surface ...

Calculus - An ocean oil well is leaking oil into the ocean at a rate of 1 m3/hr ...

Calculus - An ocean oil well is leaking oil into the ocean at a rate of 1 m3/hr ...

Calculus - An ocean oil well is leaking oil into the ocean at a rate of 1 m3/hr ...

CAL-Help on dr/dt - A circular oil slick of uniform thickness is caused by a ...

calculus - oil is leaking from a pipeline on the surface of a lake and forms an ...

CALC - The radius in meters of a circular oil slick increases at a rate of (12...

math - The radius of a circular oil slick expands at a rate of 8 m/min. a. How ...

Calculus- rates - A tanker is spilling oil into the water resulting in an oil ...