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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?  
What about a cone?  

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 <>
	From: (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

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