Scaling Intertia Tensor

Hi everyone,



I have the following problem in my hands, which I don't know how exactly to address.



Let's assume that from any CAD(Solidworks, Catia), I obtain the inertia tensor of my model (impossible to calculate by hand btw).



I_full=[Ixx Ixy Ixz

Ixy Iyy Iyz

Ixz Iyz Izz]



I know if I change the mass of my model, the inertia tensor will scale linearly with it.



But what If I scale my model to half-size, all dimensions? The mass probably goes by 1/8, since it's proportional to volume. Maybe the other factor would be 1/4 (α r^2).



So would the correct Inertia scaling factor be?:



I_half=1/4*1/8*I_full



Cheers!!