Number of Faces of a Cylinder and a ConeDate: 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 <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 |
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