If the length of a cylinder on heating increases by 2%, the area of its base will increase by 

Let length of cylinder initially be ${\ell }_{{ }^{\mathrm{\prime }}}$ coefficient of linear expansion be $\alpha ,$ and rise in temperature be

$t^{\circ }\mathrm{C},\text{ so }\mathrm{\Delta }\ell =\ell \alpha ∆t\Rightarrow \frac{\mathrm{\Delta }\ell }{\ell }\times 100=\alpha \mathrm{t}\times 100\therefore 2=\alpha ∆t\times 100$

Now, for area $\mathrm{\Delta A}=\mathrm{A\beta \Delta t}\Rightarrow \frac{\mathrm{\Delta A}}{\mathrm{A}}=\mathrm{\beta \Delta t}\Rightarrow \frac{\mathrm{\Delta A}}{\mathrm{A}}\times 100=\mathrm{\beta \Delta t}\times 100 =2\alpha ∆t\times 100 =2\times 2\% =4\%$

% change in area $=\beta \times 100=\beta ∆t\times 100=2\alpha ∆t\times 100=2(\alpha ∆t\times 100)=2\times 2=4\mathrm{\%}$