How to find the center of mass of a hemisphere of radius r, with a hole of radius r/2 within it?

Dear Amrit pal

dear consider a disk at a distance x of thickness dx whose outer radius is r' and inner radius is r/2

 where x² +r'² = r² 

 r' =√(r² -x²)

mass of the disk dm =ρ (πr'² -π(r/2)²)dx   where ρ is the dencity

                          dm =ρπ (r²-x² -r²/4)dx

                          dm =ρπ (3r²/4 -x² )dx

now center of mass = [₀∫^OC dm *x ]/ _o∫^OC dm

 where OC =√(r² -(r/2)²)

                =r√3 /2

put the value and intigrate

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