Answer:
r = 1.61 x 10^{11} m
Explanation:
energy radiated (H) = 2.7 x 10^31 W
surface temperature (T) = 11,000 k
assuming ε = 1 and taking σ = 5.67 x 10^{-8} W/m^{2}.K^{4}
we can find the radius of the star from the equation below
H = A x ε x σ x T^{4}
where area (A) = 4 x π x r^{2} (assuming it is a sphere)
therefore the equation becomes
H = 4 x π x r^{2} x ε x σ x T^{4}
2.7 x 10^31 = 4 x π x r^{2} x 1 x 5.67 x 10^{-8} x (11,000)^{4}
r = [tex]\sqrt{\frac{2.7 x 10^31}{4 x π x 1 x 5.67 x 10^{-8} x (11,000)^{4}} }[/tex]
r = 1.61 x 10^{11} m
