Editing Cylinder (section)

===Surface area===
Having radius {{math|''r''}} and altitude (height) {{mvar|h}}, the [[surface area]] of a right circular cylinder, oriented so that its axis is vertical, consists of three parts:

* the area of the top base: {{math|π''r''<sup>2</sup>}}
* the area of the bottom base: {{math|π''r''<sup>2</sup>}}
* the area of the side: {{math|2π''rh''}}

The area of the top and bottom bases is the same, and is called the ''base area'', {{math|''B''}}. The area of the side is known as the ''{{dfn|lateral area}}'', {{math|''L''}}.

An ''open cylinder'' does not include either top or bottom elements, and therefore has surface area (lateral area)
<math display=block>L = 2 \pi r h</math>

The surface area of the solid right circular cylinder is made up the sum of all three components: top, bottom and side. Its surface area is therefore
<math display=block>A = L + 2B = 2\pi rh + 2\pi r^2 = 2 \pi r (h + r) = \pi d (r + h)</math>
where {{math|1=''d'' = 2''r''}} is the [[diameter]] of the circular top or bottom.

For a given volume, the right circular cylinder with the smallest surface area has {{math|1=''h'' = 2''r''}}. Equivalently, for a given surface area, the right circular cylinder with the largest volume has {{math|1=''h'' = 2''r''}}, that is, the cylinder fits snugly in a cube of side length = altitude ( = diameter of base circle).<ref>{{citation |title=Calculus With Applications |first1=Peter D. |last1=Lax |author1-link=Peter Lax |first2=Maria Shea |last2=Terrell |publisher=Springer |year=2013 |isbn=9781461479468 |page=178 |url=https://books.google.com/books?id=dDq3BAAAQBAJ&pg=PA178 }}.</ref>

The lateral area, {{mvar|L}}, of a circular cylinder, which need not be a right cylinder, is more generally given by
<math display=block>L = e \times p,</math>
where {{mvar|e}} is the length of an element and {{mvar|p}} is the perimeter of a right section of the cylinder.{{sfn|Wentworth|Smith|1913|p=358}} This produces the previous formula for lateral area when the cylinder is a right circular cylinder.
[[File:Zylinder-rohr-s.svg|thumb|180px|Hollow cylinder]]