Posted by Liz on Sunday, June 3, 2012 at 6:21pm.
If we include the area out to x = -2, we have
v = ∫[0,6] πr^2 dy
where r = 2+x = 2+(6-y)/3 = 4-y/3
v = π∫[0,6](4-y/3)^2 dy = 56π
But we have to subtract out the interior cylinder of radius 2 and height 6, or 24π, leaving us with just 32π generated by the rotating triangle.
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