Why does a solid sphere have a smaller moment of inertia than a hollow cylinder of the same mass and radius,about an axis passing through their axes of symmetry?

(N/A) The moment of inertia $I$ of a body is given by $I = \sum m_i r_i^2$,where $m_i$ is the mass element and $r_i$ is its perpendicular distance from the axis of rotation.
For a hollow cylinder of mass $M$ and radius $R$,all its mass is distributed at a distance $R$ from the axis of symmetry. Thus,its moment of inertia is $I_{cylinder} = MR^2$.
For a solid sphere of mass $M$ and radius $R$,the mass is distributed throughout its volume,meaning most of its mass lies at a distance $r < R$ from the axis of symmetry. Its moment of inertia is $I_{sphere} = \frac{2}{5}MR^2$.
Since $\frac{2}{5}MR^2 < MR^2$,the solid sphere has a smaller moment of inertia than the hollow cylinder.