Question

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 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. 3%
• B. 4%
• C. 7%
• D. 10%

Answer 1

The correct option is A 3%

Volume of cylinder
$V=\pi r^{2}h$
or $\frac{\Delta V}{V}=2\frac{\Delta r}{r}+\frac{\Delta h}{h}$
Percentage error in volume -
$\frac{\Delta V}{V}\times 100=(2\times \frac{0.01}{2}+\frac{0.1}{5})\times 100$
$=(0.01+0.02)\times 100$
$\frac{\Delta V}{V}\times 100=\left(0.03\right)\times 100=3\%$