$\rho=\frac{ AV }{ I \ell}=\frac{\pi d ^{2} V }{4 I \ell} \quad\left( A =\frac{\pi d ^{2}}{4}\right)$

$\therefore \frac{\Delta \rho}{\rho}=\frac{2 \Delta d }{ d }+\frac{\Delta V }{ V }+\frac{\Delta I }{ I }+\frac{\Delta \ell}{\ell}$

$\frac{\Delta \rho}{\rho}=2\left(\frac{0.01}{5.00}\right)+\frac{0.1}{5.0}+\frac{0.01}{2.00}+\frac{0.1}{10.0}$

$\frac{\Delta \rho}{\rho}=0.004+0.02+0.005+0.01$

$\frac{\Delta \rho}{\rho}=0.039$

$\%$ error $=\frac{\Delta \rho}{\rho} \times 100=0.039 \times 100=3.90 \%$