The length of a cylinder is measured with a metre rod having least...

The length of a cylinder is measured with a metre rod having least count 0.1 cm . Its diameter is measured with vernier callipers having least count 0.01 cm . Given the length is 5.0 cm and diameter is 2.00 cm . Find the percentage error in the calculated value of volume.

Correct answer

Step-by-step solution

\mathrm{V}=\pi \mathrm{r}^2 \mathrm{~h}=\frac{\pi \mathrm{D}^2 \mathrm{~h}}{4} \Rightarrow \frac{\Delta \mathrm{~V}}{\mathrm{~V}}=\frac{2 \Delta \mathrm{D}}{\mathrm{D}}+\frac{\Delta \mathrm{h}}{\mathrm{h}} \frac{\Delta \mathrm{V}}{\mathrm{V}} \times 100=\left[2 \times\left(\frac{0.01}{2.00}\right)+\left(\frac{0.1}{5.0}\right)\right] \times 100=3 \%

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