We know that I=MK2
Where, I= moment of inertia, M= mass of body, K=radius of gyration.
Therefore, K=√IM
Let the initial MOI be 100I1 so K1=10I1
Now the MOI will be decreased by 36
So, final MOI after change will be I2=100I1−36I1100I1×100 so K2=8I1
So, change in radius of gyration will be ΔK=K1−K2K1=10I1−8I110I1×100=20