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A casing for a satellite is a thick spherical shell of uniform density (pictured below in cross-section). The shell is made by removing an inner sphere of material from a uniform sphere. The inner spherical cavity has 7/8 the radius of the outer surface. The moment of inertia of the sphere about a diameter before the cavity was removed was 32768 kg m2. What is the moment of inertia of the shell?

Fig: 1