Question

(b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 33 m?

Answer 1

66π m²/s ≈ 207.3 m²/s

Explanation:

The area is given by ...

A = πr²

and its rate of change is given by ...

A' = 2πr·r'

Filling in the given values, we have ...

A' = 2π(33 m)(1 m/2) = 66π m²/s ≈ 207.3 m²/s

The area of the spill is increasing at the rate of 66π m²/s ≈ 207.3 m²/s.