Question

Find the approximate change in the surface area of a cube of side $x$ metres caused by decreasing the side by $1$ percent.

Answer 1

The surface area of a cube $\left(S\right)$ with side $x$ is given by $S=6x^2$ .
$\therefore dV=\left(\frac{dS}{dx}\right)\Delta x=\left(12x\right)\Delta x$
$=\left(12x\right)(-0.01x)$ [Since given as $\Delta x=$ -1% of $x,=-0.01x$]
$=-0.12x^2$