find the volume of the solid formed when region bounded by y=x/3, y=2
and the y-axis. it is revolved about the x-axis.

the assignment was to use both the washer method and the shell method
but when i solved for the volume, i got different answers.
i think my shell method is wrong because i know i'm having difficulties
with using "dy" instead of "dx"
here's my work so far:

washer method:
R = 2, r = x/3
V=pi*integral from 0 to 6*4-(x²/9)dx
it becomes 16pi because after the integral it is
pi (4x-(x³/27)) and then i evaluated it

SHELL METHOD:
R = y, H = x = 3y
V = 2pi*integral from 0 to 6*3y²dy
it becomes 2pi(y³), evaluating it at 6
which turns out to be
432pi

but there's a huge difference between my two answers..
could you please help me find my mistake?
thanks,
christina