

The moment of inertia can now be calculated as,

b)

We have already determined the moment of inertia of a disc of radius r and thickness b in the part a) of the problem. A cone is simply a stack of several infinitesimally thin disks of gradually decreasing radii, stack on top of one another. Consider an infinitesimally thin disc of thickness dh, at a distance h from the apex of the cone O. Let the height of the cone be H. The radius of this infinitesimally thick disc will be


The total moment of inertia of the entire cone can be determined by integrating (summing) over all infinitesimally thin discs as,

Isn't it interesting to see that the moment of inertia of a cone does not depend on its height but only on the radius of its base!!
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