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?
JEE MAIN 2019, Medium
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$V = \pi {R^2}h = \frac{\pi }{4}{D^2}h$
$ = 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$
$\therefore V = 4260 \pm 80\,c{m^3}$
$ = 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$
$\therefore V = 4260 \pm 80\,c{m^3}$
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