Question

Diameter of a cylinder measured by vernier callipers of least count 0.1 mm is 2 cm. The length of the cylinder is 15 cm as measured by a scale whose least count is 1 mm. Percentage error in measurement of volume will be (Write upto two digits after the decimal point.)

Answer 1

$V=\frac{\pi D^2}{4}L\Rightarrow \frac{\Delta V}{V}=\frac{2\Delta D}{D}+\frac{\Delta L}{L}$

$\frac{\Delta V}{V}=2\times \frac{0.01}{2}+\frac{0.1}{15}$

$\%$ error $=\frac{\Delta V}{V}\times 100=1+\frac{10}{15}=1.67$