If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is
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 $2 a \%$.

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