The m.i of hollow sphere (mass =M)OF INNER RADIUS r and outer radius 2r ,having material of uniform density,about a diametric axis is

 dencity of sphere (d) = M/V

V = 4pi/3 ((2r)³ -r³)=4pi (7r³) /3

 d = 3M/4pi(7r³)         

now , consider a hollow sphere of thickness dx at a distance x from center.....   ( x is in between r to 2r..)

mass of this sphere = dm = d(4pix²dx)

                          dm= 3Mx²dx/7r³

now moment of inertia of this elemental hollow sphere is dI

dI = 2dmx² /3                                              (I_sphere (hollow) = 2mr²/3)

dI = (2/7)(M/r³)x⁴dx

now integrating

I = (2/35)(M/r³)x⁵  lim r to 2r

I = (62/35)Mr² 

approve if u like it

Approved