# CALCULUS

posted by .

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 at 0.1 m/min, and its thickness is .02 m. At that moment:
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 -

Pretty 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 -

-2.667* 10^-5

## Similar Questions

1. ### math

The radius of a circular oil slick expands at a rate of 8 m/min. a. How fast is the area of the oil slick increasing when the radius is 30 m?
2. ### calculus

oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume increases at a constant rate of 2000 cubic centimeters per minute. The oil slick takes the form of a right circular cylinder with both its …
3. ### MATH-CALC

3.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 at 0.1 m/min, and its thickness is .02 m. At that moment: a. How fast is the area …

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 at 0.1 m/min, and its thickness is .02 m. At that moment: a. How fast is the area of …
5. ### Calculus- rates

A tanker is spilling oil into the water resulting in an oil slick that is close to circular. At te time that the slick's diameter is growing at a rate of 8 ft/sec, the diameter is 250 feet. At what rate is the area of the oil sick …
6. ### CALC

The radius in meters of a circular oil slick increases at a rate of (12 - 0.3t), where t is measured in hours. Which of the following expressions would calculate the rate at which the area of the oil slick is increasing when the radius …
7. ### Calculus

An ocean oil well is leaking oil into the ocean at a rate of 1 m3/hr resulting in an oil slick in the form of a circular disk (like a quarter or dime). If the slick remains in the shape of a disk with a constant thickness of 1/100 …
8. ### Calculus

An ocean oil well is leaking oil into the ocean at a rate of 1 m3/hr resulting in an oil slick in the form of a circular disk (like a quarter or dime). If the slick remains in the shape of a disk with a constant thickness of 1/100 …
9. ### Calculus

An ocean oil well is leaking oil into the ocean at a rate of 1 m3/hr resulting in an oil slick in the form of a circular disk (like a quarter or dime). If the slick remains in the shape of a disk with a constant thickness of 1/100 …
10. ### CAL-Help on dr/dt

A circular oil slick of uniform thickness is caused by a spill of 1 cubic meter of oil. The thickness of the oil is decreasing at the rate of 0.1 cm/hr as the slick spreads. (Note: 1 cm = 0.01 m.) At what rate is the radius of the …

More Similar Questions