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I want to know the difference among "circumferential", "periphery", and "perimeter". Which is best to describe the outer surface of a round object such as a tube, a cylinder, and a can of beer.

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    I think I would call it "the surface". Do you need a more technical term? Is there a particular aspect of the outside that you're trying to describe? – stangdon Jan 22 '17 at 19:54
  • I think the word "outer surface" includes all of the top, bottom, and side surfaces. I want to distinguish these surfaces from each other. The word "side surface" may imply the top or bottom surface depending on the direction from which an object is viewed. – rama9 Jan 22 '17 at 20:01
  • The outer surface of a tube, cylinder or can of beer is one thing. That said, the ends are made of circles, filled or not. In a beer car, the ends are a round-shaped disc. A tube or cylinder may or may not have an end-cap disc. So, I dunno. In any case, the outer surface would be the exterior surface topologically speaking. If you are referring to the covers on the ends of a beer can (a round--shapend disc), that surface is also an outer surface. These objects don't have sides. A round cylindrical object doesn't have "sides". – Lambie Jan 22 '17 at 20:53
  • But none of this discussion about surfaces has anything to do with circumferences. Circles have a circumference, the distance around them. A can has a circumference in geometry. Periphery and perimeter are not terms applying to the geometer of cylinders or tubes. The periphery of something is around it but not necessarily touching it. Perimeter is for lines not surfaces, and is the distance around a non-circular object. – Lambie Jan 22 '17 at 20:58
  • If you really need to invent a term for this, try sleeve. – LawrenceC Jan 23 '17 at 1:20
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The outside surfaces of a cylinder are called it's

faces

a cylinder has 3 faces


(source: math-only-math.com)

The top and bottom can be referred to as planar surfaces whereas the body is a curved surface.

Theoretically, there is no "inside" or "outside" of the surface of a 3D object as the relationship to the boundary is described mathematically, and so the boundary is infinitesimally small

the width of a point.

The definition of a cylinder being

cylinder

In its simplest form, a cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"[1]) is the surface formed by the points at a fixed distance from a given straight line called the axis of the cylinder.)

However, practically, because of the limitations of the real world, one has the inside surface of a can which is usually coated in plastic since it comes into contact with food and the outside surface of a can which usually has a label describing the contents.

perimeter

is used to describe the path surrounding a two-dimensional shape.

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There is no common word for this in English other than "surface". In mathematics it would be called part of the "surface area" of the cylinder (excluding the top and bottom "caps").

There may be a more technical term for it, but not one I can recall from all my college math courses.

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We don't really have a standard term for "the part of the surface of a cylinder that is not one of the ends", but idiomatically we would probably call it the surface of the can (yes, technically the ends are surfaces too, but we're not speaking technically here):

For example,

...the series of arms nearest the can-revolving devices over which the label is drawn and between which and the surface of the can the label is pressed...

Or we might call it the side or sides of the can or bottle:

He toyed with the sticky label on the side of the bottle...

With pliers, crimp the sides of the can at the bottom at four places around the can.

It's usually plural, sides, if you're talking about the whole outside surface of the can or more than one place on it. Again, yes, technically it's one surface, but this is informal speech.

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The "outside" surface of a cylinder can be called the "outside". This surface happens to be "convex".

If you are describing the stresses and strains in the material, three directions are most important:

  1. The "axial" direction is parallel to the axis of the cylinder.
  2. The "radial" direction is from the inside of the cylinder toward the outside of the cylinder. In other words, this direction "radiates" from the axis of the cylinder. The radial direction is perpendicular to the axial direction.
  3. The "circumferential" or "tangential" direction is perpendicular to both the axial direction and the radial direction. At any given point on the cylinder, this direction is parallel to a line that is "tangent to" a circular cross-section of the cylinder. A "hoop" is a physical object that is a circular cross-section of a cylinder. Hoops are sometimes used to reinforce cylinders, so the stress in this direction is often called the "hoop stress".

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