Editing Cylinder (section)

=== Right circular hollow cylinder (cylindrical shell)===

A ''right circular hollow cylinder'' (or ''{{dfn|cylindrical shell}}'') is a three-dimensional region bounded by two right circular cylinders having the same axis and two parallel [[Annulus (mathematics)|annular]] bases perpendicular to the cylinders' common axis, as in the diagram.

Let the height be {{math|''h''}}, internal radius {{math|''r''}}, and external radius {{math|''R''}}.  The volume is given by subtracting the volume of the inner imaginary cylinder (i.e. hollow space) from the volume of the outer cylinder:  
<math display=block>
V = \pi \left( R ^2 - r ^2 \right) h
= 2 \pi \left ( \frac{R + r}{2} \right) h (R - r).
</math>
Thus, the volume of a cylindrical shell equals {{nobr|2{{pi}}&thinsp;×}}&thinsp;{{nobr|average radius&thinsp;×}}&thinsp;{{nobr|height&thinsp;×}}&thinsp;thickness.{{sfn|Swokowski|1983|p=292}}

The surface area, including the top and bottom, is given by
<math display=block> A = 2 \pi \left( R + r \right) h + 2 \pi \left( R^2  - r^2 \right). </math>
Cylindrical shells are used in a common integration technique for finding volumes of solids of revolution.{{sfn|Swokowski|1983|p=291}}