Concept:

Volume of a cylinder of radius ‘r’ and height h is given by

V = πr² h

Or

\(V = \pi {\left( {\frac{D}{2}} \right)^2}h\)

\(\left[\because {d = 2r \Rightarrow r = \frac{d}{2}} \right]\) 

\(V = \frac{1}{4}\left( {\pi {D^2}h} \right)\)

Where D is the diameter of circular surface

Calculation:

Given,

Diameter of the cylinder, D = 12.6 ± 0.1 cm

Height of the cylinder, h = 34.2 ± 0.1 cm

Here, D = 12.6 cm and h = 34.2 cm

\(V = \frac{\pi }{4} \times {\left( {12.6} \right)^2} \times \left( {34.2} \right)\)

\(V = \frac{\pi }{4} \times 158.76 \times 34.2\)

\(V = \frac{\pi }{4} \times 5429.592\)

V = 1357.398 × π

V = 1357.398 × 3.14

V = 4262.22 cm³

V = 4260 (in three significant numbers)

We know that,

ΔD = ± 0.1 and Δh = ± 0.1

Now, error calculation can be done as

\(\frac{{{\rm{\;\Delta }}V}}{V} = 2\left( {\frac{{{\rm{\Delta }}D}}{D}} \right) + \frac{{{\rm{\Delta }}h}}{h} = \frac{{2 \times 0.1}}{{12.6}} + \frac{{0.1}}{{34.2}}\) 

\(\frac{{{\rm{\Delta }}V}}{V} = 0.0158 + 0.0029\) 

\(\frac{{{\rm{\Delta }}V}}{V} = 0.01879\) 

ΔV = (0.01879) × (4262.22)

ΔV = 79.7 ≈ 80 cm³

∴ For proper significant numbers, volume reading will be V = 4260 ± 80 cm³