Question:
If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is
(a) $2 a \%$
(b) $\frac{a}{2} \%$
(c) $3 a \%$
(d) none of these
Solution:
(a) 2a%
Let x be the side of the cube and y be its surface area.
$\frac{\Delta x}{x} \times 100=a$
Also, $y=6 x^{2}$
$\Rightarrow \frac{d y}{d x}=12 x$
$\Rightarrow \frac{\Delta y}{y}=\frac{12 x}{y} \times d x=\frac{2}{x} \times \frac{a x}{100}$
$\Rightarrow \frac{\Delta y}{y} \times 100=2 a$
Hence, the error in the surface area is $2 a \%$.