(Solved): The coordinate axes in the figure run through the centroid of a solid wedge parallel to the labele ...

The coordinate axes in the figure run through the centroid of a solid wedge parallel to the labeled edges. The wedge has \( a=6, b=9 \), and \( c=6 \). The solid has constant density \( \delta=1 \). The square of the distance from a typical point \( (x, y, z) \) of the wedge to the line \( L: z=0, y=9 \) is \( r^{2}=(y-9)^{2}+z^{2} \) Calculate the moment of inertia of the wedge about \( \mathrm{L} \).