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.
the volume of a cone = 1/3 pi a²h
answer will be (3/10)Ma²