A rectangular block is heated from 0°C to 100°C. The percentage increase in its length is 0.10%. What will be the percentage increase in its volume ?

Given $\mathrm{\Delta l}/\mathrm{l}=0\cdot 10\mathrm{\%}=0\cdot 001\text{ and }\mathrm{\Delta T}={100}^{\circ }\mathrm{C}$
Now     $\frac{\mathrm{\Delta l}}{\mathrm{l}}=\mathrm{\alpha \Delta T}$
or       $0\cdot 001=\mathrm{\alpha }\times 100\text{ or }\mathrm{\alpha }={10}^{-5}{/}^{\circ }\mathrm{C}$
Further      $\mathrm{\gamma }=3\mathrm{\alpha }=3\times {10}^{-5}{/}^{\circ }\mathrm{C}$
$\therefore \frac{\mathrm{\Delta V}}{\mathrm{V}}=\mathrm{\gamma \Delta T}=\left(3\times {10}^{-5}\right)\left(100\right)=3\times {10}^{-3}$
or    $\frac{\mathrm{\Delta V}}{\mathrm{V}}\times 100=\left(3\times {10}^{-3}\right)\left(100\right)=0\cdot 30\mathrm{\%}$