The moment of inertia of a sphere with uniform density about an axis through its center is 2/5MR^2= 0.400MR^2. Satellite observations show that the earth's moment of inertia is 0.3308MR^2. Geophysical data suggest the earth consists of five main regions: the inner core (r= 0 to r= 1220km) of average density 12900kg/m^3, the outer core (r=1220km to r= 3480km) of average density 10900kg/m^3, the lower mantle (r= 3480km to r= 5700km) of average density 4900 kg/m^3, the upper mantle (r= 5700km to r= 6350km) of average density 3600 kg/m^3, and the outer crust and oceans (r= 6350km to r= 6370km) of average density 2400 kg/m^3.

Use the given data to calculate the earth's moment of inertia in terms of MR^2