Question

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

Answer 1

The volume of a cube $\left(V\right)$ with side $x$ is given by $V=x^3$ .
$\therefore dV=\left(\frac{dV}{dx}\right)\Delta x=\left(3x^2\right)\Delta x$
$=\left(3x^2\right)\left(0.001x\right)$ [Since given $\Delta x=$ 1% of $x,=0.01x$]
$=0.03x^3$
Hence, the approximate change in the volume of the cube is $0.03x^3$ m${}^3$