mass moment of inertia

1. The problem statement, all variables and given/known data

for the mass moment of inertia, why did they use Ix/Iy and not Iz?
2. Relevant equations

Ix=Iy= 1/12 m (3(r^2) + (h^2))
Iz= 1/2 m (r^2)

3. The attempt at a solution

Attached Images
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