Associated Topics || Dr. Math Home || Search Dr. Math

### Number of Faces of a Cylinder and a Cone

```
Date: 29 Jan 1995 18:34:41 -0500
From: D'Ann James Douglas
Subject: Faces

If you have a cylinder, how many faces does it have?

Thank you,  D'Ann

This is a teacher question.
```

```
Date: 30 Jan 1995 17:28:34 GMT
From: Dr. Math
Subject: Re: Faces

Hello there!

To tell you the truth, I wasn't really sure on this one.  See,
you're right to wonder about using the word "faces" to describe
curved surfaces.  I figured I'd ask some folks at the Geometry
Forum (specifically Steve Weimar), and here's the reply.

Date: Mon, 30 Jan 1995 10:25:06 -0500
To: Ken Williams <ken@sccs.swarthmore.edu>
From: steve@mathforum.org (Stephen Weimar)
Subject: Re: faces (fwd)

Hello, Steve!

Say, I was going to send a reply to this person, saying that
they both have one face, but then I got to thinking that I'd
be less comfortable talking about faces on a figure that's
not a polyhedron.  Is that kosher?  I figured I'd ask you
Geometry People.

Right.  My understanding, and I checked this with Don, is
that the term "faces"  is usually reserved for the flat
surfaces of polyhedra.  On the other hand, with a more
sophisticated concept of boundary one can extend the
concept of faces.

In the case of the cone and cylinder I suppose one could
say they have 2 and 3 respectively (assuming solid ends).

So the answer is that it's kind of a grey area; if you want to talk
about these objects having faces at all, then a cylinder would
have 3 faces or 1 face, depending on whether you had endcaps
on it or not, and a cone would have 2 or 1.

-Ken "Dr." Math
```
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search