Final answer:
The average density of a neutron star with the same mass as the sun but a smaller radius can be calculated using the formula: Average density = Mass / Volume. Using the given values, we can calculate the average density to be approximately 2.63 × 10^17 kg/m³.
Step-by-step explanation:
The average density of a neutron star with the same mass as the sun but a radius of only 20.0 km can be calculated using the formula:
Average density = Mass / Volume
Since the radius of the neutron star is given, we can use the formula for the volume of a sphere:
Volume = (4/3) * π * Radius^3
Using the mass of the sun (M = 1.99 × 10^30 kg) and the given radius (20.0 km = 20,000 m), we can calculate the average density.
The average density of the neutron star is approximately 2.63 × 10^17 kg/m³.