Here, Coefficient of linear expansion of copper, $\alpha = 1.70 \times 10^{-5} \mathrm{K}^{-1}$$\Delta T = 227 - 27 = 200^{\circ}\mathrm{C}$Therefore, coefficient of superficial expansion of copper$\beta = 2\alpha = 2 \times 1.70 \times 10^{-5} \mathrm{K}^{-1}$$\beta = 3.40 \times 10^{-5} \mathrm{K}^{-1}$Area of hole at 27°C,$S_{1}= \frac{\pi D_{1}^{2}}{4}= \frac{\pi}{4}(4.24)^{2} \ \mathrm{cm}^{2}$$=\pi \times 4.4944 \ \mathrm{cm}^{2}$If $D_2$ cm is the diameter of the hole at $227^{\circ}\mathrm{C}$, then Area of the hole at $227^{\circ}\mathrm{C}$,$S_{2}= \frac{\pi D_{2}^{2}}{4} \ \mathrm{cm}^{2}$Increase in area $=S_{2}-S_{1}=S_{1} \beta \Delta T$ $\frac{\pi D_{2}^{2}}{4}=\pi \times 4.4944 \times (1+3.4 \times 10^{-5}(227-27) )$$D_{2}^{2}=(4.24)^{2} \times (1.0068)$$\Rightarrow D_{2}=4.2544 \ \mathrm{cm}$Change in diameter $=D_{2}-D_{1}$$=4.2544-4.24$$=0.0144 \ \mathrm{cm}$