Question

A solid cone of uniform density ρ has a base radius a and a height h. Now the top h/2 is cut by a plane parallel to the base and removed. For the remaining part of the truncated cone, calculate:
a. Center of the mass
b. Moment of inertial about its symmetry axis

Answer 1

this should prove helpful.

web.mit.edu/8.13/8.13c/references-fall/aip/aip-handbook-section2c.pdf

or just do the required integrals for yourself...
google can provide helpful examples and derivations.