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

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

$\begin{aligned} \therefore d V &=\left(\frac{d V}{d x}\right) \Delta x & & \\ &=\left(3 x^{2}\right) \Delta x & & \\ &=\left(3 x^{2}\right)(0.01 x) & &[\text { as } 1 \% \text { of } x \text { is } 0.01 x] \\ &=0.03 x^{3} & & \end{aligned}$

Hence, the approximate change in the volume of the cube is $0.03 x^{3} \mathrm{~m}^{3}$.