Question

An offshore oil well is leaking oil and creating a circular oil slick. If the radius of the slick is growing at a rate of 2 miles/hour, find the rate at which the area is increasing when the radius is 3 miles. (The area of a disc of radius r is

Answer 1

37.7 mi²/h

Explanation:

The area formula is ...

A = πr²

Differentiating with respect to time gives ...

dA/dt = 2πr·dr/dt

Filling in the given values, we have ...

dA/dt = 2π(3 mi)(2 mi/h) = 12π mi²/h

The area is increasing at the rate of about 37.7 mi² per hour.