Question

The length of a cylinder is measured with a meter rod having least count $0.1$cm. Its diameter is measured with Vernier calipers having least count $0.01cm$. Given that length is $5.0cm$ and radius is $2$cm. Find the percentage error in the calculated value of the volume.

Answer 1

Volume of cylinder $V=\pi r^{2}L$

$\therefore$ Percentage error in volume

$\Rightarrow \frac{\Delta V}{V}\times 100=\frac{2\Delta r}{r}\times 100+\frac{\Delta l}{l}\times 100$

$=2\left(\frac{0.01}{2.0}\right)\times 100+\frac{0.1}{5.0}\times 100$

$=(1+2)=3$ .