Question

The length of a cylinder is measured with a meter rod having least count 0.1 cm. Its diameter is measured with venier 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

• A. 1%
• B. 2%
• C. 3%
• D. 4%

Answer 1

Answer: (C)

3%

Answer 2

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

Percentage error in volume

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

$= \left( 2 \times \frac{0.01}{2.0} \times 100 + \frac{0.1}{5.0} \times 100 \right)$ $= (1 + 2)\%$ =$3\%$