Answer:
A) 5.1*10^10m B) 5.4*10^6m
Explanation:
Utilizing the formula for surface radiation P (energy per second in Watts) = emissivity constant * surface area * Stefan-Boltzmann constant * Temperature in Kelvin^4 *
2.7*10^31 = 1* 5.67*10^-8*A*11000^4
Rearranging to solve for A = 2.7*10^31 / (5.67*10^-8*1.46*10^16) = 0.3261*10^23m^2
Assuming the shape is spherical, the surface area is = 4πR^2 (radius of Rigel)
R = √(0.3261*10^23 / 4*π) = 5.1 * 10^10m
B) repeating the same calculation
2.1 *10^23 = 1*A*5.67*10^-8*10000^4 where A is the surface area of Procyon
Rearranging gives A = 2.1*10^23/(5.67*10^-8*10^16)
A = 0.37*10^15
Assuming the star is spherical;
A = 4πR^2 where R is Procyon's radius
R = √(0.37*10^15/4π) = 5.4*10^6m