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  4. The length of a cylinder is measured with a metre rod having least count 0.1 cm. Its diameter is measured with vernier calipers having least count 0.01 cm. If the length and diameter of the cylinder are 5.0 cm and 2.00 cm, respectively, then the percentage error in the calculated value of volume will be

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Q. The length of a cylinder is measured with a metre rod having least count $0.1\, cm$. Its diameter is measured with vernier calipers having least count $0.01\, cm$. If the length and diameter of the cylinder are $5.0\, cm$ and $2.00\, cm$, respectively, then the percentage error in the calculated value of volume will be

Physical World, Units and Measurements

Solution:

Volume of cylinder $\left(V\right)=\pi r^{2}l$
$\frac{\Delta V}{V}\times100=2\times\frac{\Delta r}{r}\times 100+\frac{\Delta l}{l}\times 100$
$=2\times\frac{0.01}{2}\times100+\frac{0.1}{5}\times100$
$=1\%+2\%=3\%$