Question

An open can of oil is accidentally dropped into a lake; assume the oil spreads over the surface as a circular disk of uniform thickness whose radius increases steadily at the rate 10 cm/sec. At the moment when the radius is 1 meter, the thickness of the oil slick is decreasing at the rate 4 mm/sec; how fast is it decreasing when the radius is 2 meters? (Watch the units!)

Answer 1

−0.0005 m/sec.

Explanation:

Let us denote the volume of the can as V

let us denote the radius of the circular disc in lake as r

Let us denote the thickness of the circular disc as h

But we know the volume of the can as πr^2h then we can calculate How fast it is decreasing when the radius is 2 m

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION