I have to find the volume of a bounded region as it rotates around the Y-axis. My points are y=6; x=-2; x=2; and y=0. What would be the steps to solving this and the solution? Thank you!
2026-04-11 23:45:49.1775951149
Finding the volume of a rotating cross section
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A rectangle formed by vertices $(-2,0), (2,0), (2,6) \text{ and } (-2,6)$ is symmetrically positioned around the y-axis, and when rotated, gives a cylinder. Simply plug in $r=2-(-2)=4$ and $h=6-0=6$ in $V=\pi r h^2 $ and this gives the answer $96\pi$ sq. units.