The diameter and height of a cylinder are measured by a meter scale to be \(12.6 \pm 0.1\, cm\) and \(34.2  \pm  0.1\, cm\), respectively. What will be the value of its volume in appropriate significant figures?

\(\begin{array}{l}
V = \pi {R^2}h = \frac{\pi }{4}{D^2}h\\
\,\,\,\,\,\,\, = 4260\,c{m^2}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{\Delta V}}{V} = 2\frac{{\Delta D}}{D} + \frac{{\Delta h}}{h}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {2 \times \frac{{0.1}}{{12.6}} + \frac{{0.1}}{{34.2}}} \right)V\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2 \times 426}}{{12.6}} + \frac{{426}}{{34.2}}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 67.61 + 12.459 = 80.075\\
\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,V = 4260 \pm 80\,c{m^3}
\end{array}\)