The density of water at $20°\mathrm{C}\text{ is }998 \mathrm{kg}/{\mathrm{m}}^3$  and at $40°\mathrm{C} is 992 kg/m^3$. The coefficient of volume expansion of water is 

$\text{ As }{\rho }_{T_2}=\frac{{\rho }_{T_1}}{(1+\gamma \Delta T)}=\frac{{\rho }_{T_1}}{1+\gamma \left(T_2-T_1\right)}$

$\text{ Here, }{T}_1=20°\mathrm{C},T_2=40°\mathrm{C}$

${\mathrm{\rho }}_{20}=998 \mathrm{kg}/{\mathrm{m}}^3,{\mathrm{\rho }}_{40}=992 \mathrm{kg}/{\mathrm{m}}^3$

$$\begin{gathered} \therefore 992=\frac{998}{1+\mathrm{\gamma }(40-20)} \\ 992=\frac{998}{1+20\mathrm{\gamma }} \end{gathered}$$

$992(1+20\mathrm{\gamma })=998$

$1+20\mathrm{\gamma }=\frac{998}{992} \text{ or } 20\mathrm{\gamma }=\frac{998}{992}-1=\frac{6}{992}$

$\mathrm{\gamma }=\frac{6}{992}\times \frac{1}{20}=3\times {10}^{-4}/{}^{\circ }\mathrm{C}$