Question

The percentage error in measuring the side of a cube is $0.5$ percentage error in volume is

• A. $1/2$
• B. $1$
• C. $3/2$
• D. $2$

Answer 1

The correct option is C $3/2$

Volume of cube = $x^3$

$\frac{\Delta v}{\Delta x}=\frac{3x^2}{2}$

$\frac{\Delta v}{v}=\frac{3x^2}{2}\frac{\Delta x}{x^3}$

$\Rightarrow \frac{\Delta v}{v}\times 100\%=\frac{3}{2}\frac{\Delta x}{x}\times 100\%$

$\Rightarrow (\%$ error in volume)=$\frac{3}{2}(\%$ error in side of cube)

% error in volume = $\frac{3}{2}\left(\frac{1}{2}\right)$

$\therefore$ percentage error in volume $\Rightarrow \frac{3}{2}\%\left(1.5\%\right)$

Option C is correct.