Question

what is the derivation of moment of inertia of solid cone?

Answer 1

Consider a uniform solid cone having circular base of radius a, height h and mass M.
u should know the mass 
now we can say
 (X,Y,Z) = (0,0,h/4) which is correct.
For the moment of inertia
 use the definition of I =  pb² dV where p = mass pert unit volume, and b is the distance from the axis.
 We know
the volume of a cone = 1/3 pi a²h
so
answer will be (3/10)Ma²

Answer 2

Rotational inertia is important in almost all physics problems that involve mass in rotational motion. It is used to calculate angular momentum and allows us to explain (via conservation of angular momentum) how rotational motion changes when the distribution of mass changes.