Derivation of the atomic nucleus formula

[Bestfrog]

Does anyone know the heuristic derivation of this formula? $$R=r_{0} \cdot A^{\frac{1}{3}}$$ with $R$ the atomic nucleus, $r_0$ the radius of a nucleon (proton or neutron) and $A$ the number of nucleons.
I know that there is a sperimental derivation, but I would find a theoretic/heuristic derivation.

 

[.Scott]

I take it the "R" is the "radius" of the atomic nucleus. So all they're saying is that the total volume for radius R is the same as the the total of the volumes for each nucleon. Cubing both sides gives you $R^3 = A r_0^3$. Then multiple both sides by 4/3 pi and you have volume=volume.

 

[Bestfrog]

Thank you!