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Paper Cylinder

Paper model cylinder cylinder cylinder

Cylinder:

Net cylinder

In common usage, a cylinder is taken to mean a right circular cylinder, as in the picture.
If the cylinder has a radius r and height h, then its volume is given by:
V = pi  r^2  h

Defenition right circular cylinder
A cylinder which has bases aligned one directly above the other.  Bases that are circles.
Defenition cylinder
A three-dimensional geometric figure with parallel congruent bases. The bases can be shaped like any closed plane figure (not necessarily a circle) and must be oriented identically.

More definitions see:
mathwords.com  cylinder
mathworld.com cylinder
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