Calculus HELP Please?

Question

A ruptured oil tanker causes a a circular oil slick on the surface of the ocean. When its radius is 150 meters, the radius on 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 the oil spilled remains fixed. How fast is the thickness of the slick decreasing?


Please Help

Answer 1

a. The area is A = pi r^2. dA/dt = 2 pi r * dr/dt.

r = 150 meters. dr/dt = .1 meter/minute. Plug those values in.

b. Thickness * area = volume = a constant that you can compute by plugging in the known values.

From this you get thickness = (another constant) * r^(-2)..

d thickness/dt = -2 * (that latter constant) ^ r^(-3).

Plug in your numbers and you're done!

Answer 2

1) r = 150 m
dr/dt = 0.1 m/min
h(thickness) = 0.02 m

a) A(r) = pi x (r^2)

dA/dt = 2 x pi x r x (dr/dt)

= 2 x pi x (150) x (0.1)

= 30 pi (m^2)/min

b)-1

V(r) = pi x (r^2) x h ; V remains constant so solve for volume.

= pi x (150)^2 x (0.02)

= 450 pi (m^3)/min

Sorry, still working on part B, but what is printed right above should be where you start for part B.