Mathematics - Application of Derivative Question with Solution | TestHub

Volume V of a cube of side $x$ is given by $\begin{array}{rl}\mathrm{V}& ={\mathrm{x}}^3\\ \Rightarrow \frac{\mathrm{dv}}{\mathrm{dx}}& =3{\mathrm{x}}^2\end{array}$ Let the change in $x$ be $\Delta x=K\%$ of $x=\frac{kx}{100}$ Now, the change in volume, $\begin{array}{c}\Delta \mathrm{V}=\left(\frac{\mathrm{dV}}{\mathrm{dx}}\right)\Delta \mathrm{x}=3{\mathrm{x}}^3(\Delta \mathrm{x})\\ =3{\mathrm{x}}^2\left(\frac{\mathrm{kx}}{100}\right)=\frac{3{\mathrm{x}}^3\cdot \mathrm{k}}{100}\end{array}$ $\therefore$ Approximate change in volume $=\frac{3{\mathrm{kx}}^3}{100}=\frac{3\mathrm{k}}{100}\cdot {\mathrm{x}}^3$ $=3\mathrm{K}\%$ of original volume