The volume of the wire is given by, \\\\(V = \\pi r^2 L\\\\)Thus density of the wire, \\\\(\\rho = \\dfrac{m}{\\pi r^2 L}\\\\)Taking log and then differentiate: \\\\(\\implies \\dfrac{\\Delta \\rho}{\\rho} \ imes 100 = \\dfrac{\\Delta m}{m} \ imes 100 + 2 \\dfrac{\\Delta r}{r} \ imes 100 + \\dfrac{\\Delta L}{L} \ imes 100\\\\)\\\\(\ herefore \\\\) \\\\( \\dfrac{\\Delta \\rho}{\\rho} \ imes 100 = \\dfrac{0.003}{0.3} \ imes 100 + 2 \\dfrac{0.005}{0.5} \ imes 100 + \\dfrac{0.06}{6} \ imes 100 = 4\\\\)%.\\\\(\\implies \\\\) Percentage error in density is \\\\(4\\\\)%.