Sketch the region enclosed by the lines x=0 x=6 y=2 and y=6. identify the vertices of the region. revolve the region around the y-axis. identify the solid formed by the revolution calculate the volume of the solid. leave the answer in terms of pi.

The region describes a rectangle, and the vertices are just the intersections of pairwise-chosen lines, e.g. and intersect at (0, 2), and intersect at (0, 6), and so on.

The four vertices are then (0, 2), (0, 6), (6, 2) and (6, 6).

Since the line coincides with the -axis, revolving the region about this axis will generate a cylinder of radius 6 and height 6 - 2 = 4, so you can expect the volume to be



We can compute a volume integral to verify this: using the shell method, we have