We apply the parallel axis theorem to calculate these moments of inertia.
For the X axis, we have:
\[I_x = \frac{1}{12} \times 4 \times 6^3 + 4 \times 6 \times 2^2 - \left(\frac{\pi}{4} \times 1^2 + \pi \times 1 \times 4^2\right)\]
Solving this gives us \(I_x
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