Review 5: Solids of Revolution - Summary

In this module, we have examined two different ways of partitioning a solid of revolution in order to create a definite integral representing its volume.  The two methods depend on if we partition in the direction of the axis of rotation (this creates the "disk" method of example one) or in the direction perpendicular to the axis of rotation (the ``shell'' method of example two).  The decision of which of the two methods to use depends usually on the curve bounding the area being rotated. In general, if slicing the region in vertical slices looks "simpler" than in horizontal slices, you should use the shell method if the axis of rotation is a vertical line, and the disk method if the axis of rotation is a horizontal line. Similarly, if slicing the region in horizontal slices looks "simpler" than in horizontal slices, you should use the shell method if the axis of rotation is a horizontal line, and the disk method if the axis of rotation is a vertical line.