Question

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

• A. $2a$
• B. $\frac{a}{2}$
• C. $3a$
• D. None of the above

Answer 1

Answer: (A)

$2a$

Surface area of cube $S=6x^2$
$\Rightarrow logS=log6+2logx$
On differentiating we get,
$\frac{\Delta S}{S}=2\frac{\Delta x}{x}$
$\frac{\Delta S}{S}=2a\%$