Resistance of a wire of length 1 m, diameter 1 mm is 2.2 Ω. Calculate its resistivity and conductivity.

Resistance of a wire of length 1 m, diameter 1 mm is 2.2 Ω. Calculate its resistivity and conductivity.
Solution:
Given,
resistance , $R$ = 2.2 $\mathrm{\Omega }$
length, $l$ = 1 m
diameter, $d$ = 1 mm
radius, $r$ = $\frac{d}{2}$ = 0.5 $\times$ 10${}^{-3}$ m
resistivity, $\rho$ = ?
conductivity, $\sigma$ = ?
Now,
$$\begin{array}{rl}R& =\frac{\rho l}{A}\\ 2.2& =\frac{\rho \times 1}{\pi \times (0.5\times {10}^{-3}{)}^2}\\ \rho & =2.2\times \pi \times (0.5\times {10}^{-3}{)}^2\\ \therefore \rho & =1.73\times {10}^{-6}\mathrm{\Omega }m\end{array}$$ Again,
$$\begin{array}{rl}\sigma & =\frac{1}{\rho }\\ & =\frac{1}{1.73\times {10}^{-6}}\\ \therefore \sigma & =5.78\times {10}^5{\mathrm{\Omega }}^{-1}{m}^{-1}\end{array}$$ Hence, the resistivity is $1.73\times {10}^{-6}$ $\mathrm{\Omega }m$ and conductivity is $5.78\times {10}^5$ ${\mathrm{\Omega }}^{-1}{m}^{-1}$.