Explanation

(b) Experimentally it is found that the volume of a nucleus is directly proportional to its mass number. From this it is concluded that the density of each nucleus is uniform, it does not depend on the size of the nucleus.
It the nucleus is assumed to be a sphere of radius $R$ and its mass number is $A$, then volume of nucleus $V = \frac{4}{3}\pi R^{3}.$
Thus, $\ \ \ \ \ \ \ \ \ \ \ \ \frac{4}{3}\pi R^{3} \propto \ A\ or\ R^{3} \propto \ A$
Or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ R\ \propto \ A^{1/3}$
$ie,$ the radius of nucleus is directly proportional to the cube root(or $\frac{1}{3}$ power) of its mass number A.
Aliter
Nuclear radius
$\ \ \ \ \ \ \ \ \ R = R_{0}A^{1/3}$
$\therefore\ \ \ \ \ \ \ \ \ R \propto \ A^{1/3}$