A circular disc of radius $3$ cm is heated; its radius grows at $0.05$ cm/s. The approximate rate of increase of its area when the radius is $3.2$ cm is

1. $A=\pi r^2$, so $\dfrac{dA}{dt}=2\pi r\dfrac{dr}{dt}$. 2. Given $\dfrac{dr}{dt}=0.05$, $r=3.2$. 3. $\dfrac{dA}{dt}=2\pi(3.2)(0.05)=0.320\pi$. 4. Trap $0.640\pi$ drops the factor $0.05$ vs $0.1$. _Source: NCERT Class 12 Mathematics Ch 6 "Application of Derivatives", p.33_