Astronomy midterm question: supergiants larger than same-temperature main-sequence stars?

Astronomy 210 Midterm 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

24gurl: How do astronomers conclude that a supergiant star is larger than a main-sequence star of the same temperature?
Roger: The supergiant star is more luminous than the main sequence star of the same temperature. The only way that a supergiant could be more luminous than the main sequence star is if it is larger, the luminosity is proportional to the star's area...

Discuss whether or not if this answer is correct, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

[*] answers.yahoo.com/question/index?qid=20100217203829AADBeYk.

Solution and grading rubric:

• p:
  Correct. Uses Stefan-Boltzmann law and/or interprets H-R diagram to show that supergiants must be larger than main sequence stars of the same temperature in order to be more luminous than the main sequence stars.
  
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors.
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzman law.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzman law.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:Section 70158
Exam code: midterm02s3Ar
p: 16 students
r: 5 students
t: 3 students
v: 9 students
x: 0 students
y: 1 student
z: 0 students

A sample "p" response (from student 1210), with a bonus illustration: