Question

If there is an error of $k$ in measuring the edge of a cube, then the percent error in estimating its volume is

• A. $k$
• B. $3k$
• C. $\frac{k}{3}$
• D. none of these

Answer 1

The correct option is B $3k$

Volume of cube$V=x^3$
$\frac{dV}{dx}=3x^2$
Percentage error in measuring side $=k$
$\Rightarrow \frac{\delta x}{x}=\frac{k}{100}$
$\delta x=\frac{xk}{100}$
Approximate error in estimating volume $=dV=\left(\frac{dV}{dx}\right)\delta x=3x^2\frac{xk}{100}$
Percentage error in estimating volume$=\frac{dV}{V}\times 100=3k$