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## Homework Statement

Find the volume generated by rotating the area bounded by [itex] y^2 = 8x, x = 2 [/itex] and the x-axis about the y-axis.

## Homework Equations

Volume of cylinder, volume of disk.

## The Attempt at a Solution

I think this can be solved by subtracting the 'empty' volume from the volume of a cylinder of radius 2:

[tex] \pi r^2h - \int_0^4 \frac{\pi y^2}{8}\,dy [/tex]

I get an answer of [itex] \pi 40/3 [/itex] but the solution provided is [itex] 128/5\pi [/itex].

I'm sure my arithmetic is not that far off :-)

What did I do wrong?

Thanks,

Sheldon