When the mass number A of a nucleus increases, which of the...

The radius of a nucleus is given by $R = R_{0}A^{1/3}$, where $A$ is the mass number and $R_{0}$ is a constant.

The volume of the nucleus is $V = \dfrac{4}{3}\pi R^3 = \dfrac{4}{3}\pi R_{0}^3 A$.

The mass of the nucleus is approximately $M = m A$, where $m$ is the average mass of a nucleon.

The density of the nucleus is $\rho = \dfrac{M}{V} = \dfrac{m A}{\dfrac{4}{3}\pi R_{0}^3 A} = \dfrac{m}{\dfrac{4}{3}\pi R_{0}^3}$.

Since the density is independent of the mass number $A$, it remains unchanged when $A$ increases. Volume, mass, and total binding energy all depend on $A$ and will change.