$($a$)$ If $A$ is the area of a circle with radius $r$ and the circle expands as time passes, find $\frac{dA}{dt}$ in terms of $\frac{dr}{dt}.$

$\frac{dA}{dt}=(,)\frac{dr}{dt}$

$($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 $2\frac{m}{s},$ exactly how fast $($in $\frac{m^2}{s}$ the area of the spill increasing when the radius is $40m?$

$\frac{m^2}{s}$