Density D of nuclear matter varies with nucleon number A as

$D∝A^0$

$ R = K A^{frac{1}{3}}$

$ \Rightarrow V = \frac{4\pi}{3} R^3 \propto \frac{4\pi K}{3}A$

$\Rightarrow \text{Density } D = \frac{M}{V} = \frac{A M_p}{\frac{4K\pi}{3}A} = \frac{3A M_p}{4K\pi A} = \frac{3M_p}{4K\pi}$

$ \Rightarrow \text{ Density is independent of A}$