Need Help!! in a hurry

• Apr 2nd 2008, 07:36 PM
mathlete
Need Help!! in a hurry
A ruptured oil tanker causes a circular oil slick on the surface of the ocean. When its radius is 110 meters, the radius of the slick is expanding by 0.6 meter/minute and its thickness is 0.03 meter.

(a) At that moment, 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 when the radius is 110 meters?

this one probably seems harder than im making it out to be, but i need help, the thickness part freaks me out...thanks

mathlete
• Apr 2nd 2008, 08:45 PM
CaptainBlack
Quote:

Originally Posted by mathlete
A ruptured oil tanker causes a circular oil slick on the surface of the ocean. When its radius is 110 meters, the radius of the slick is expanding by 0.6 meter/minute and its thickness is 0.03 meter.

(a) At that moment, how fast is the area of the slick expanding?

$A=\pi r^2$

$\frac{d}{dt}A=2 \pi r \frac{dr}{dt}$

Quote:

(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 when the radius is 110 meters?

$V=A \times h$

where $h$ is the thickness.

$\frac{d}{dt}V=A \frac{dh}{dt}+h \frac{dA}{dt}=0$

RonL