$r=(0.5 \pm 0.005) \; mm$

$l=(4 \pm 0.04) \; cm$

$\rho=\frac{m}{V}$

$\Rightarrow \frac{\Delta \rho}{\rho}=\frac{\Delta m}{m}+\frac{2 \Delta r}{r}+\frac{\Delta l}{l}$

(Volume of cylinder $=\pi r^{2} l$ )

$=\frac{0.006}{0.6}+\frac{2 \times 0.005}{0.5}+\frac{0.04}{4}$

$100 \times \frac{\Delta \rho}{\rho}=4 \times 10^{-2} \times 100$

$\frac{\Delta \rho}{\rho} \times 100=4 \%$