Question

Suppose the resistance of a wire varies inversely as the area of its cross-section. Write a relation between resistance and area of cross-section

Answer 1

Suppose the radius of the wire is $r$. Then the area of its cross-section is $\pi r^2$. If $R$ is the resistance, we are given
$R\propto \frac{1}{\pi r^2}$
Hence
$R=\frac{k}{\pi r^2}$ or $k=R\pi r^2$.