A thick spherical shell has inner radius a and outer b. The material has resistivity $\rho$. When a potential difference is applied between the inner and outer surfaces, its resistance is

Resistance of thin elementary shell of radius r is $\mathrm{dR}=\frac{\rho \left(\mathrm{dr}\right)}{4\pi r^2}$

As all the elementary shells are in series between inner and outer surfaces, total resistance

 $\mathrm{R}={\int }_{\mathrm{a}}^{\mathrm{b}} \frac{\rho \left(\mathrm{dr}\right)}{4\pi {\mathrm{r}}^2}=\frac{\rho }{4\pi }\left|-\frac{1}{r}\right|=\frac{\rho (b-a)}{4\pi ab}$