Question

A cuboid has volume $V=1\times 2l\times 3l$ where $1$ is the length of one side. If the relative percentage error in the measurement of $l$ is $1\%$, then the relative percentage error in measurement of $V$ is

• A. $18\%$
• B. $6\%$
• C. $3\%$
• D. $1\%$

Answer 1

The correct option is C $3\%$

$V=6l^3$

$\Rightarrow \frac{\Delta V}{V}\times 100=3\times \frac{\Delta l}{l}\times 100$

$\Rightarrow \frac{\Delta V}{V}\times 100=3\times 1=3\%$

$\therefore \%errorinV=3\%$

Hence,

option $\left(C\right)$ is correct answer.