Question

The lenght of a cylinder is measured with a meter rod having least count $0.1cm$. Its diameter is measured with vernier calipers having least count $0.01cm$. Given that lenght is $5.0cm$ and radius is $2.0cm$. The percentage error in the calculated value of the volume will be

• A. $2\%$
• B. $4\%$
• C. $3\%$
• D. $1\%$

Answer 1

The correct option is C $3\%$

As we know,
Volume of cylinder $V=\pi r^{2}l$
Therefore, Percentage error in volume is given by,
$\frac{\Delta V}{V}\times 100=\frac{2\Delta r}{r}\times 100+\frac{\Delta l}{l}\times 100\frac{\Delta V}{V}\times 100=(2\times \frac{0.01}{2.0}\times 100+\frac{0.1}{5.0}\times 100)\frac{\Delta V}{V}\%=(1+2)\%\frac{\Delta V}{V}\%=3\%$