A stone dropped into a lake makes circular waves whose radius grows at $4$ cm/s. When the radius is $10$ cm, the enclosed area is increasing at the rate of

1. $A=\pi r^2$. 2. By Chain Rule: $\dfrac{dA}{dt}=2\pi r\dfrac{dr}{dt}$. 3. Given $\dfrac{dr}{dt}=4$, $r=10$. 4. $\dfrac{dA}{dt}=2\pi(10)(4)=80\pi$. _Source: NCERT Class 12 Mathematics Ch 6 "Application of Derivatives", p.2_