Final answer:
The radius of the event horizon of a black hole formed by a burned out star with a mass of at least three solar masses is approximately 8.87 kilometers.
Step-by-step explanation:
The radius of the event horizon of a black hole depends on its mass. Astrophysical theory suggests that a burned out star will collapse under its own gravity to form a black hole when its mass is at least three solar masses. The radius of the event horizon, also known as the Schwarzschild radius, can be calculated using the formula:
r = 2Gm/c^2
where r is the radius of the event horizon, G is the gravitational constant, m is the mass of the black hole, and c is the speed of light in a vacuum.
Given that the mass of the black hole is at least three solar masses (m = 3 x 1.99 x 10^30 kg), we can substitute the values into the formula:
r = 2 x 6.674 x 10^-11 m^3/kg/s^2 x (3 x 1.99 x 10^30 kg) / (2.998 x 10^8 m/s)^2
Simplifying the equation gives:
r ≈ 8.87 x 10^3 meters
Therefore, the radius of the event horizon of the black hole formed by a burned out star with a mass of at least three solar masses is approximately 8.87 kilometers.