Example 1: the diameter and length of a metal cylinder measured with the help of vernier callipers of least count 0.01 cm are 1.22 cm and 5.35 cm. Calculate the volume V of the cylinder and uncertainty in it. Solution: Given data is
Diameter d = 1022 cm with least count 0.01 cm
Length l = 5.35 cm with least count 0.01 cm
Absolute uncertainty in length = 0.01 cm
%age uncertainty in length = (0.01 cm / 5.53 cm ) X (100 / 100) = 0.2%
Absolute uncertainty in diameter = 0.01 cm
%age uncertainty in diameter = (0.01 cm / 1.22 cm) X (100 / 100)= 0.8%
As volume V = (πd^{2}l) / 4
Therefore total uncertainty in V = 2 (%age uncertainty in diameter)
+ (%age uncertainty in length)
=2 × 0.8 + 0.2 = 1.8%
Then V = 3.14 X (0.61 cm)^{2} X 5.35 cm / 4 = 6.2509079 cm³ with 1.8% uncertainty
Thus V = (6.2 ± 0.1) cm³
Where 6.2 cm³ is calculated volume and 0.1 cm³ is the uncertainty in it.