Why is moment of interia of ring more than cylinder?

Question

1/2mr0^2 + 1/2mri^2 = Inertia of the ring. Why is it plus and not negative? the intergral should be subtraction. no?

Thanks

Answer 1

If the mass is the same the moment of inertia of the ring is larger because the mass is farther from the axis. If the density is the same it is smaller.