The relationship between resistance R and resistivity [tex]\rho[/tex] is
[tex]R= \frac{\rho L}{A} [/tex] (1)
where L is the length of the wire and A is the cross-sectional area.
In our problem, the radius of the wire is half the diameter: r=1 mm=0.001 m, so the cross-sectional area is
[tex]A=\pi r^2 = \pi (0.001 m)^2=3.14 \cdot 10^{-6} m^2[/tex]
The length of the wire is L=20 m and the resistance is [tex]R=0.25 \Omega[/tex].
By re-arranging equation (1), we can find the resistivity of the wire:
[tex]\rho = \frac{RA}{L}= \frac{(0.25 \Omega)(3.14 \cdot 10^{-6} m^2)}{(20 m)} = 3.93 \cdot 10^{-8} \Omega \cdot m[/tex]
