Space between two concentric conducting spheres of radii a and $\mathrm{b}(\mathrm{b}>\mathrm{a})$ is filled  with a medium of resistivity $\mathrm{\rho }$. The resistance between the two spheres (in ohm) will be

For a elemental shell of radius X and thickness dx.

Resistance, $\mathrm{dR}=\mathrm{\rho }\frac{\mathrm{l}}{\mathrm{A}}$ $\Rightarrow \mathrm{dR}=\mathrm{\rho }\frac{\mathrm{dx}}{4{\mathrm{\pi x}}^2}$

So resistance of complete arrangement is 

$\mathrm{R}=\underset{\mathrm{a}}{\overset{\mathrm{b}}{\int }}\mathrm{dR}=\underset{\mathrm{a}}{\overset{\mathrm{b}}{\int }}\mathrm{\rho }\frac{\mathrm{dx}}{4{\mathrm{\pi x}}^2}=\frac{\mathrm{\rho }}{4\mathrm{\pi }}\underset{\mathrm{a}}{\overset{\mathrm{b}}{\int }}{\mathrm{x}}^{-2}\mathrm{dx}$

$\Rightarrow \mathrm{R}=\frac{\mathrm{\rho }}{4\mathrm{\pi }}{\left(\frac{{\mathrm{x}}^{-1}}{-1}\right)}^{\mathrm{b}}=\frac{\mathrm{\rho }}{4\mathrm{\pi }}{{\left(-\frac{1}{\mathrm{x}}\right)}_{\mathrm{a}}}^{\mathrm{b}}$

$=\frac{\mathrm{\rho }}{4\mathrm{\pi }}\left(-\frac{1}{\mathrm{b}}-\left(-\frac{1}{\mathrm{a}}\right)\right)$

$=\frac{\mathrm{\rho }}{4\mathrm{\pi }}\left(\frac{1}{\mathrm{a}}-\frac{1}{\mathrm{b}}\right)\mathrm{ohm}$