luminosity of star

Question

Star A has a radius 11 times the Sun's radius. If its temperature is the same as the Sun's, then the luminosity of Star A is  times that of the Sun.

Answer 1

You would use the Stefan-Boltzmann equation (http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html) for luminosity and take a ratio of the luminosity of Star A to the luminosity of the Sun. All quantities cancel except radii, so you end up the 11 squared on the right side. Thus Star A has 121 times the luminosity of the Sun.