With cylinder I have:
body = Cylinder({{-l/2, 0, 0}, {l/2, 0, 0}}, r);
((ScriptCapitalI) = (Rho) MomentOfInertia(body,
Assumptions -> l > 0 && w > 0 && h > 0)) // MatrixForm;
m Cancel((ScriptCapitalI)/((Rho) Volume(body))) // MatrixForm(*Code from MMA help*)
(*{{(m*r^2)/2, 0, 0}, {0, (m*(l^2 + 3*r^2))/12, 0}, {0, 0, (m*(l^2 + 3*r^2))/12}}*)
But how do this with half cylinder?