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Tatiana [17]
3 years ago
11

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
Mathematics
1 answer:
Genrish500 [490]3 years ago
5 0

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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