## Cylinder

A cylinder is a solid of circular Cross-Section in which the centers of the Circles all lie on a single Line. The cylinder was extensively studied by Archimedes in his 2-volume work On the Sphere and Cylinder in ca. 225 BC.

A cylinder is called a right cylinder if it is straight'' in the sense that its cross-sections lie directly on top of each other; otherwise, the cylinder is called oblique. The surface of a cylinder of height and Radius can be described parametrically by

 (1) (2) (3)

for and . These are the basis for Cylindrical Coordinates. The Surface Area (of the sides) and Volume of the cylinder of height and Radius are
 (4) (5)

Therefore, if top and bottom caps are added, the volume-to-surface area ratio for a cylindrical container is
 (6)

which is related to the Harmonic Mean of the radius and height .

See also Cone, Cylinder-Sphere Intersection, Cylindrical Segment, Elliptic Cylinder, Generalized Cylinder, Sphere, Steinmetz Solid, Viviani's Curve

References

Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 129, 1987.