A neutron star possesses a density equivalent to that of nuclear...

The density of nuclear matter is approximately $\rho \approx 3 \times 10^{17} \text{ kg/m}^3$.

Given the mass of the neutron star, $M = 4.0 \times 10^{30} \text{ kg}$.

Assuming the neutron star is spherical, its density is given by:

$\rho = \dfrac{M}{\dfrac{4}{3}\pi R^3}$

Rearranging for the radius $R$:

$R^3 = \dfrac{3M}{4\pi \rho}$

Substituting the values:

$R^3 = \dfrac{3 \times 4.0 \times 10^{30}}{4\pi \times 3 \times 10^{17}}$

$R^3 = \dfrac{10^{13}}{\pi} \approx 3.18 \times 10^{12} \text{ m}^3$

Taking the cube root:

$R \approx 1.47 \times 10^4 \text{ m} \approx 15 \text{ km}$