Question

The percentage error in the measurement of radius r of a sphere is 0.1% then the percentage error introduced in the measurement of volume is ______.

Options

• 0.1%

• 0.2%

• 0.25%

• 0.3%

Answer 1

The percentage error in the measurement of radius r of a sphere is 0.1% then the percentage error introduced in the measurement of volume is 0.3%.

Explanation:

\[\frac{\Delta\mathrm{r}}{\mathrm{r}}\times100=0.1\%\mathrm{and}\mathrm{V}=\frac{4}{3}\pi\mathrm{r}^3\]
\[\begin{aligned} \text{Percentage error in volume} & =\frac{\Delta V}{V}\% \\ & =\frac{3\Delta r}{r}=0.3\% \end{aligned}\]