AP Calculus AB and BC glossary
Solid of revolution
A solid of revolution is the three-dimensional shape swept out when a plane region is rotated about a line. Its volume is computed by integrating cross-sectional areas, using the disk method, the washer method, or the shell method.
The choice of method is really a choice of slice direction. Disks and washers slice perpendicular to the axis of rotation, so they integrate with respect to the axis variable; shells slice parallel to it.
Use a washer rather than a disk whenever the region does not touch the axis of rotation, because the gap becomes a hole through the solid.
Radii are distances
Rotating about a line other than an axis changes every radius. The radius is always the distance from the slice to the axis, so it becomes an expression like rather than .
Appears in: Unit 8: Applications of Integration