Problem 2E

2. (a) If $A$ is the area of a circle with radius $r$ and the circle expands as time passes, find $d A / d t$ in terms of $d r / d t$.

(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 $1 \mathrm{~m} / \mathrm{s}$, how fast is the area of the spill increasing when the radius is $30 \mathrm{~m}$ ?

 

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