Moment of inertia of a solid cone about its vertex
= Moment of inertia of a solid cone about its vertex
For a uniform solid cone of height $l$, base radius $R$, and mass $M$, whose symmetry axis points from vertex to base, the centre of mass lies at $3l/4$ from the vertex. The principal moments at the vertex are
$$
I_1=I_2=\frac{3M}{20}(R^2+4l^2),
\qquad I_3=\frac{3MR^2}{10}.
$$