The moment of inertia of a cylindrical shell of external and internal radii R and r and mass M about a vertical axis perpendicular to its length $\mathcal{l}$ is-

(A) $\mathrm{M}\left(\frac{{\mathrm{R}}^2+{\mathrm{r}}^2}{2}\right)+\frac{\mathrm{M}{\mathcal{l}}^2}{12}$        
(B) $\mathrm{M}\left(\frac{{\mathrm{R}}^2+{\mathrm{r}}^2}{2}\right)+\frac{\mathrm{M}{\mathcal{l}}^2}{3}$    
(C) $\mathrm{M}\left(\frac{{\mathcal{l}}^2+3{\mathrm{R}}^2-3{\mathrm{r}}^2}{12}\right)$               
(D) $\mathrm{M}\left(\frac{{\mathrm{R}}^2+{\mathrm{r}}^2}{4}\right)+\frac{\mathrm{M}{\mathcal{l}}^2}{12}$