the neutrons and protons are both Nucleons ,the total number of Nucleon is A.
the nuclues is form by both proton and neutron.
since the radii of proton is equal to neutrons.
therefore :
Nproton +N neutron = A
therefore
the total volume is
4/3 * Pi *r^3 * A
As we know the radus of Nuclues is R.
therefore
the total volume of Nuclues is
4/3* Pi * R ^3
since Nuclues is formed by nucleons.i.e total of protons and neutrons.
therefore
4/3* Pi * R^3 = 4/3 * Pi *r^3 * A
R^3 = r^3 A
R= (r^3 A )^ 1/3
R= r A^1/3