Wherein a surface area is not found

So, today Dr. Nevard finally gave us back a quiz from quite a while ago. It had one problem that was just finding the surface area of a certain solid of revolution (x^2/3+y^2/3=1, first quadrant, about either axis). Still, afterward, noone could come to a consensus as to the answer. Well, a few people could. So, today we finally got it back. Here were everybody's answers:

Me: π√2
Marc: 4π/5
Rajesh: 3π/2
Emily: 3
Tom, Jacob, and Choketsu: 3π²/16
Hyun-soo and Chris: 3π√2/4
Fan: 12π/5
James: 3/2
Avi: 3π/4
Ben: Effectively, did not answer. Left his answer in the form of an incredibly nasty (and almost certainly wrong) iterated integral which he was waiting for his TI-89 to evauluate.

The correct answer? 6π/5.

...yay.

Number of rational numbers: 2
Number of rational multiples of π: 4
Number of rational multiples of π²: 3
Number of rational multiples of π√2: 3

-Sniffnoy, who still maintains that his answer was the coolest