Question

It is required to find the volume of a rectangular block. A Vernier calipers is used to measure he length, width and height of the block. The measure values are found to be 1.37 cm, 4.11 cm, and 2.56 cm respectively.

Answer 1

The measured (nominal) volume of the block is,

Therefore,

V = l x w x h

= (1.37 × 4.11 × 2.56) cm³ .

= 14.41 cm³

However, each of these measurement has an uncertainty of + 0.01 cm, the least count of the Vernier caliper. We can say that the values of length, width and height should be written as

l = (1.37 cm ± 0.01 cm)

w = (4.11 cm ± 0.01 cm)

h = ( 2.56 cm ± 0.01 cm)

We thus find that the lower limit, of the volume of the block, is given

V_min= 1.36 cm × 4.10 cm × 2.55 cm

= 14.22 cm²

This is 0.19 cm³ lower than the (nominal) measured value.

The upper limit can also be calculated:

V_min = 1.38 cm × 4.12 cm × 2.57 cm

= 14.61 cm³

This is 0.20 cm3 higher than the measured value. As a practical rule, we choose the higher of these two deviations (from the measured value) as the uncertainty, in our result. We, therefore, should report the volume of the block as (14.41 cm³ ± 0.20 cm³ ).