Prove that the density of nuclear matter is same for all nuclei.

Volume of a nucleus $\displaystyle = \frac{4}{3}\pi R^{3}$$\displaystyle = \frac{4}{3}\pi \left(R_{0}A^{\frac{1}{3}}\right)^{3}$$\displaystyle = \frac{4}{3}\pi R_{0}^{3}A$$\displaystyle \rho = \dfrac{\text{mass of nucleus}}{\text{volume of nucleus}}$$\displaystyle = \dfrac{mA}{\frac{4}{3}\pi R_{0}^{3}A} = \dfrac{3m}{4\pi R_{0}^{3}}$