A circular plate expands when heated from a radius of 5 cm to 5.06 cm. The approximate increase in area is

$$\begin{gathered} \text{ Given }r=5,\delta r=5.06-5=0.06\text{. Now }A=\pi r^2 \\ \delta A\cong \frac{dA}{dr}\delta r=2\pi r\delta r \\ \text{ The increase in }A\text{ is }\delta A=2\pi r\delta r=2\pi \left(5\right)\left(0.06\right)=0.6\pi \text{ sq. cm } \\ \text{ The percentage increase in area is } \\ \frac{\delta A}{A}\times 100=\frac{2.\pi \cdot r.\delta r}{\pi r^2}\times 100=2.\frac{\delta r}{r}\times 100=\frac{2\left(0.06\mathrm{\pi }\right)}{5}\times 100=2.4\mathrm{\pi } \end{gathered}$$