Question

If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is
(a) 2a%

(b) $\frac{a}{2}\%$

(c) 3a%

(d) none of these

Answer 1

(a) 2a%

Let x be the side of the cube and y be its surface area.

$$\begin{gathered} \frac{∆x}{x}\times 100=a \\ \mathrm{Also},y=6x^2 \\ \Rightarrow \frac{dy}{dx}=12x \\ \Rightarrow \frac{∆y}{y}=\frac{12x}{y}\times dx=\frac{2}{x}\times \frac{ax}{100} \\ \Rightarrow \frac{∆y}{y}\times 100=2a \\ \mathrm{Hence},\mathrm{the}\mathrm{error}\mathrm{in}\mathrm{the}\mathrm{surface}\mathrm{area}\mathrm{is}2a\%. \end{gathered}$$