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 mile
s/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
1 answer:
Answer:
37.7 mi²/h
Step-by-step 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.
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