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Inertia and center of mass of a shell Find $$I _ { z }$$ and the center of mass of a thin shell of density $$\delta ( x , y , z ) = z$$ cut from the upper portion of the sphere $$x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 25$$ by the plane $$z = 3$$ .
$$( \overline { x } , \overline { y } , \overline { z } ) = ( 0,0,49 / 12 ) , I _ { z } = 640 \pi$$