I asked two different people and one person got 256/9 by taking parabolic slices, and another person got 8*pi by taking slices that are circles. Who is right and why?

Hello, eskimogenius!
I asked two different people and one person got 256/9 by taking parabolic slices,
and another person got 8*pi by taking slices that are circles.
Who is right and why?
Why did the second person use circular slices?
The problem said parabolic cross-sections, right?