The approximate change in the volume of a cube of side x metres

The volume of a cube $(V)$ of side $x$ is given by $V=x^{3}$.

$\therefore d V=\left(\frac{d V}{d x}\right) \Delta x$

$=\left(3 x^{2}\right) \Delta x$

$=\left(3 x^{2}\right)(0.03 x) \quad[$ As $3 \%$ of $x$ is $0.03 x]$

$=0.09 x^{3} \mathrm{~m}^{3}$

Hence, the approximate change in the volume of the cube is $0.09 x^{3} \mathrm{~m}^{3}$.

The correct answer is $\mathrm{C}$.