Question

x = (y − 9)2, x = 16; about y = 5
the region bounded by the given curves is rotated about the specified axis Find V of the resulting solid

Answer 1

Are you switching names? Derek, Lisa, Ron ???
I just did this one when you were Ron, check below, but I used discs
since at the time you did not specify what method.

I think oobleck likes doing these using discs, let's hope he will look at it

Answer 2

The graphs intersect at (16,13) and (16,5)
so using shells of thickness dy,
v = ∫2πrh dy
where r = y-5 and h = 16-x = 16-(y-9)^2
v = ∫[5,13] 2π(y-5)(16-(y-9)^2) dy = 2048π/3