$\frac{{\Delta {l}}}{{l}}\, = \,\frac{{0.01}}{{4.0}}\, = \,0.0025$

$r\,\, = \,\,(0.250\,\, \pm \,\,0.001\,)\,\,cm\,\,$

$\frac{{\Delta r}}{r}\, = \,\frac{{0.001}}{{0.250}}\, = \,0.004$

$m\,\, = \,\,(6.25\,\, \pm \,\,0.01)\,\,g\,\,\,\,$

$\frac{{\Delta m}}{m} = \frac{{0.01}}{{6.25}}\, = \,0.0016$

density = mass/volume $ = \,\,\frac{m}{{\pi {r^2}{l}}}\,$

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

$\frac{{\Delta \rho }}{\rho } \times \,100\,\% $ $ = \left( {\frac{{\Delta m}}{m} \times \,100} \right)\%  + $ $2\left( {\frac{{\Delta r}}{r} \times 100} \right)\%  + \left( {\frac{{\Delta {l}}}{{l}} \times \,100} \right)\% $

$ = \,(0.0025\, \times \,100)\,\% \,\, + \,\,2(0.004\, \times \,100)\% \,\, + \,\,(0.0016\, \times 100)\,\% $

$\, = \,0.25\% \, + \,0.8\%  + \,0.16\,\%  = \,1.21\% $