Question

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

Answer 1

Let y be the surface area of the cube.

$$\begin{gathered} y=6x^2 \\ \mathrm{We}\mathrm{have} \\ \frac{△x}{x}\times 100=1 \\ \mathrm{Now}, \\ \frac{dy}{dx}=12x \\ \Rightarrow △y=dy=\frac{dy}{dx}dx=12x\times \frac{x}{100}=0.12x^2{\mathrm{m}}^2 \\ \mathrm{Hence},\mathrm{approximate}\mathrm{change}\mathrm{in}\mathrm{the}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cube}\mathrm{is}0.12x^2{\mathrm{m}}^2. \end{gathered}$$