A wire of length 1 m and of radius 0.1 mm has a resistance of 100Ω.The resistivity of the material is

Use the equation to get the wire's resistance. This equation explains the relationship between the wire's resistance, resistivity of the wire's material, length, and cross-sectional area.
The phrase for the wire's resistance is

$R=\rho \frac{L}{A}\dots \dots \text{ (1) }$
Here, L stands for the wire's length, R for its resistance, and A for its cross-sectional area and $\rho$ is the substance of the wire's resistance.
The formula for the circle's surface area is
$A=\pi r^2\dots \dots \text{ (2) }$
Here, A denotes the circle's area, while r denotes its radius.

Given,

length of wire = 1m

radius of wire $r=0.1mm=(0.1mm)\left(\frac{{10}^{-3}m}{1mm}\right)={10}^{-3}m$

resistance of wire = $100\Omega$

Cross-sectional area of the wire $A=(3.14)\left(\right(0.1mm){\left(\frac{{10}^{-3}}{1mm}\right))}^2=3.14\times {10}^{-8}{m}^2$Resistivity $\rho =\frac{RA}{L}$

$$\begin{gathered} \rho =\frac{\left(100\Omega \right)(3.14\times {10}^{-8}{m}^2)}{1m} \\ \Rightarrow \rho =3.14\times {10}^{-6}\Omega .m \end{gathered}$$

Hence option C is the correct answer.