What is the resistivity of a perfect conductor?

The coefficient of linear expansion of the material of a resistor is $\alpha$. Its temperature coefficient of resistivity and resistance are $\alpha_\rho$ and $\alpha_R$ respectively. Then the correct relation is:

$A$ given piece of wire of length $l$ and radius $r$ and resistance $R$ is stretched uniformly to a wire of radius $\frac{r}{2}$. Its new resistance is .................. $R$.

The following four wires are made of the same material and are at the same temperature. Which one of them has the highest electrical resistance?

$A$ rectangular carbon block has dimensions $1.0 \ cm \times 1.0 \ cm \times 50 \ cm$. The resistance is to be measured first between the two square ends and then between the two rectangular ends. If the resistivity of carbon is $3.5 \times 10^{-5} \ \Omega \cdot m$,find the values of the resistances in both cases respectively.

At what temperature $(^oC)$ will the resistance of a copper wire become three times its value at $0^oC$? (Given: Temperature coefficient of resistance of copper at $0^oC$ is $\alpha = 4 \times 10^{-3} / ^oC$)