The #18 tungsten has a radius of [tex]r=5.1\cdot 10^{-4}m[/tex]. The resistivity of the tungsten at [tex]20^{\circ}[/tex] is [tex]\rho=5.6\cdot 10^{-8} \Omega m[/tex]. The formula that relates resistance and resistivity is
[tex]R=\rho \frac{L}{\pi r^2} [/tex]
where L is the length of the wire and [tex]\pi r^2[/tex] its section. Therefore, we can calculate L:
[tex]L= \frac{R \pi r^2}{\rho}= \frac{10\Omega \cdot \pi (5.1\cdot 10^{-4}m)^2}{5.6\cdot 10^{-8} } =145.8 m[/tex]
