Final answer:
Using the Stefan-Boltzmann law and the given power radiated and radius of a star, we calculate the surface temperature to be approximately 6.27 × 10^3 K, which is option A.
Step-by-step explanation:
To find the temperature of the surface of the star, we can use the Stefan-Boltzmann law, which states that the power radiated per unit area of a black body is proportional to the fourth power of its temperature.
The formula for this law is P = σAT^4, where P is the power radiated, σ is the Stefan-Boltzmann constant, A is the surface area, and T is the temperature in Kelvin.
In this case, we are given the total power (P) radiated by the star as 5.32 × 10^26 W and the radius (r) of the star as 6.95 × 10^8 m. We can calculate the surface area (A) of the star using the formula for the surface area of a sphere, A = 4πr^2.
Substituting the known values into the Stefan-Boltzmann formula and solving for T, we get:
A = 4π(6.95 × 10^8 m)^2
T = √[4(5.32 × 10^26 W) / (4π(6.95 × 10^8 m)^2 × 5.67 × 10^-8 W/m^2 · K^4)]
After calculating T, we find that the closest value that fits one of the answer choices is 6.27 × 10^3 K, which corresponds to option A.