Question

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

Answer 1

Given $d=12.6\pm 0.1\text{cm}\text{and}h=34.2\pm 0.1\text{cm}$

Volume of cylinder is
$V=\frac{\pi }{4}{d}^{2}h=\frac{\pi }{4}\left(12.6{)}^2\right(34.2)\approx 4260{\text{cm}}^3$

Hence using,

$\frac{\Delta V}{V}=\frac{2\Delta d}{d}+\frac{\Delta h}{h}$

$\frac{\Delta V}{4260}=\frac{0.2}{12.6}+\frac{0.1}{34.2}$

$\Delta V=80{\text{cm}}^3$
The value of its volume in appropriate significant figures is $4260\pm 80{\text{cm}}^3$