**(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt.**

**(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 30 m?**

**Answer:**

**(a)**

A= π*r^2
dA/dt = 2π*r*(dr/dt)

**(b)**

rate of area (dA/dt) when r = 30 m

relationship: A = πr^2

so dA/dt = 2πr(dr/dt) from part a

dA/dt = 2π(30)(1)

= 60π m^2/s