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Is it true that the volume of the nucleus is approximately proportional to the mass number of the atom?
This sentence is correct.

Because I read an article before that said:

The size of the nucleus is usually considered to be verified by experiments, and experiments are completed by Coulomb scattering experiments of a particle. For example, in the original method, Rutherford bombarded aluminum foil with particle A. This is the conclusion that there exists R = R0A 1/3 for kernel radius r and mass number a. ..

In the traditional scheme of measuring the size of atomic nuclei (see any college physics book containing atomic nuclei), there are two assumptions, namely:

First, the volume v of the nucleus is approximately proportional to the mass number;

Please refer to the attached drawings.