Explanation

(c) $V = \ \ \pi r^{2}l$
$\frac{\mathrm{\Delta}V}{V} = \frac{\mathrm{\Delta}\left( \pi r^{2}l \right)}{\pi r^{2}l}\ \ or\ \frac{\mathrm{\Delta}V}{V} = \ \frac{r^{2}\mathrm{\Delta}l + 2rl\mathrm{\Delta}r\ }{r^{2}l}$
$\frac{\mathrm{\Delta}V}{V} = \frac{\mathrm{\Delta}l}{l} + \frac{2\mathrm{\Delta}r}{r}\ $
But $\sigma = - \ \frac{\mathrm{\Delta}r/r}{\frac{\mathrm{\Delta}l}{l}} = - \ \frac{\mathrm{\Delta}r/r}{- 2\frac{\mathrm{\Delta}r}{r}} = 0.5$