Astronomy final exam question: hottest supergiants the biggest stars possible?

Astronomy 210 Final Exam, spring semester 2017
Cuesta College, San Luis Obispo, CA

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

Pdg: Are the hottest supergiants the biggest stars possible on an H-R diagram?
qcp: They are.

Discuss whether this answer is correct or incorrect, 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=20170323215116AASJ9GS.

Solution and grading rubric:

• p:
  Correct. Discusses how the Stefan-Boltzmann law and/or H-R diagram shows that the hottest supergiant is not necessarily the largest possible star, as the cooler supergiants would be larger.
• 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. At least discussion demonstrates understanding of the Stefan-Boltzmann law and/or H-R diagram. May have instead conflated "brightest" with "biggest" that the hottest supergiants would be the most luminous supergiants possible, or that the hottest main-sequence stars would be the most luminous stars possible.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use the Stefan-Boltzmann law and/or H-R diagram.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on the Stefan-Boltzmann law and/or H-R diagram.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Section 30674
Exam code: finalnmSS
p: 8 students
r: 3 students
t: 4 students
v: 2 students
x: 1 student
y: 0 students
z: 0 students

Section 30676
Exam code: finalSBr6
p: 16 students
r: 1 student
t: 12 students
v: 5 students
x: 1 student
y: 0 students
z: 2 students

A sample "p" response (from student 1866):
Another sample "p" response (from student 6850):
A sample "t" response (from student 8959):
Another sample "t" response (from student 9433):