cylinder (geometry)

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In geometry, a prism with a circular cross-section. In everyday use, the term applies to a right cylinder, in which the curved surface is perpendicular to the base.

As it is a prism, the volume (V) of a cylinder is area of cross-section (πr²) × height (h), or

V = πr²h

where r is the radius of the base and h is the height of the cylinder.

Its total surface area (A) = the curved surface area + the area of both circular ends. To find the curved surface area, the hollow cylinder area should be imagined stretched flat to form a rectangle:

Curved surface area = circumference × h, or 2πr × h

Area both circular ends = 2 × πr²

So A = 2πr² + 2πrh

and by factorizing:

A = 2πr(h + r)

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