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 0.01 cm . Given that length is 5.0 cm . and radius is 2.0 cm . The percentage error in the calculated value of the volume will be
Text Solution
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Volume of cylinder \(V = \pi r^{2} l\)
Percentage error in volume
\(\frac{\Delta V}{V} \times 100 = \frac{2 \Delta r}{r} \times 100 + \frac{\Delta l}{l} \times 100\)
\(= \left( 2 \times \frac{0.01}{2.0} \times 100 + \frac{0.1}{5.0} \times 100 \right)\) = (1 + 2)\% = 3%
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