Hi i was wondering, if the sphere is divided into 5 spherical shells, each shell has a different density and each shell is of equal thickness

My question is: Can I calculate the moments of inertia for each shell by subtracting the moment of inertia of the sphere inside it, from the entire sphere. Does this calculate the moment of inertia for that individual shell and then I can add them up to get the entire sphere's moment of inertia? I hope i've been clear. Just not sure about adding/subtracting moments... thanks!

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