Find the approximate change in the volume $V$ of a cube of side $x$ metres caused by increasing the side by $1\%$.

We have $V = {x^3} \Rightarrow \cfrac{{dV}}{{dx}} = 3{x^2}$
and $\Delta V = \left( {\cfrac{{dV}}{{dx}}} \right)\Delta x = 3{x^2}\left( {\cfrac{x}{{100}}} \right)$

$= \cfrac{{3{x^3}}}{{100}}$

Therefore the change in volume $= 0.03\,{x^3}\,{m^3}$