Question

the length of a uniform rod is 100.0 and radius is 1.00cm if length is measured with a meter rod having least count 1mm and radius is measured with callipers having least count 0.1mm the pecentage error in calculated volume of cylinder is 2.1% HOW?

Answer 1

Volume of the cylinder is given as $\pi r^{2}h$

Now, Percentage error in volume

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

Now we can write

Maximum error in radius $\frac{\Delta r}{r}=\frac{0.1}{10}=0.01$

Maximum error in length $\frac{\Delta l}{l}=\frac{1}{1000}=0.001$

Now we can write

$\frac{\Delta V}{V}\times 100=2\times 0.01\times 100+0.001\times 100$

After solving

$\frac{\Delta V}{V}\times 100=2.1\%$

Hence error in the calculation of volume is 2.1 %