Question

The percentage error in the surface area of a cube with edge x cm, when the edge is increased by $11\%$ is _________.

• A. $11$
• B. $22$
• C. $10$
• D. $44$

Answer 1

Answer: (B)

$22$

Surface area of cube $=$ S $=6x^2$
$\therefore \frac{dS}{dt}=12x\frac{dx}{dt}$
Side of cube increase $11\%$.
$\therefore \frac{dx}{dt}=11\%$ increment in side
$=\frac{11x}{100}$
$\therefore \frac{dx}{dt}=12\left(\frac{11x}{100}\right)$
$=6\left(\frac{22}{100}\right)x^2$
$=6x^2\left(\frac{22}{100}\right)$
$=22\%$ in surface area
$\therefore$ Surface area increase $22\%$.