A hollow cylindrical conductor has length of \( 3.14 \, \mathrm{m} \), while its inner and outer diameters are \( 4 \, \mathrm{mm} \) and \( 8 \, \mathrm{mm} \) respectively. The resistance of the conductor is \( n \times 10^{-3} \, \Omega \). If the resistivity of the material is \( 2.4 \times 10^{-8} \, \Omega \, \mathrm{m} \). The value of \( n \) is ______.
