A wire has a mass (0.3± 0.003) g radius (0.5± 0.005)mm and length (6 ± 0.06)cm . The maximum percentage error in the measurement of its density is

Density $\mathrm{\rho }=\frac{\mathrm{m}}{{\mathrm{\pi r}}^2\mathrm{L}}.$
$\therefore \frac{\mathrm{\Delta \rho }}{\mathrm{\rho }}\times 100=\left(\frac{\mathrm{\Delta m}}{\mathrm{m}}+2\frac{\mathrm{\Delta r}}{\mathrm{r}}+\frac{\mathrm{\Delta L}}{\mathrm{L}}\right)\times 100=\left[\frac{0.003}{0.3}+2\times \frac{0.005}{0.5}+\frac{0.06}{6}\right]\times 100=4\%.$
After substituting the values, we get the maximum percentage error in density = 4%.
Hence, the correct option is (4).