Faces, Edges and Vertices of 3D Shapes
Aug 04, · A cone has one face. It is a three-dimensional shape with a circular base, one side and one vertex. Faces can be identified as the flat surfaces on a three-dimensional figure. There are a variety of cone types, but all of them only have one face. Cones can be right circular cones or oblique circular cones. Right circular cones are symmetrical with the axis passing through the center of the cone at a . Solid cone. A cone is a shape with a circular base and a single face that ends in a point. Face. This face is shaped like a funnel.
We had previously wuat several questions that touched on this, but had not really addressed the issue. But we whar to state our definition when we do so vone it is not necessarily something that others will have defined the same shaep. Mathematicians fave accustomed to making up definitions for their particular context like this. Again, the book is giving definitions suitable for a polyhedron, but applying them inconsistently to non-polyhedra.
I responded again, after referring to w previous answer:. She copied in two responses to the question. I will just quote pieces of it that relate most directly to our present issue of definition:.
He talks about convex polyhedra, then about topology, where straightness and flatness are irrelevant, concluding that the intuitive definitions make sense, with caution. The only purpose I see for using these terms is to be able to talk about an object, not necessarily fone to whaat math with it.
But to do that, the terms should have universal definitions, as these do not. We also see that without a universal definition, mathematicians happily just define them ad hoc. I have varied on which approach I prefer. That is also why books disagree.
I have taught courses in Mathematics for Elementary Ls several times, and observed that their what is joshua ledet doing now did not ask about faces of cylinders; there was no need to do so.
This wisdom needs to be passed down to the elementary curricula themselves. Or, we might call any surface a face. The question would be, why do we need to use the terms? Or, as mathematicians often do, definitions embedded in the documents. Your email address will not be published. This site uses Akismet to reduce spam. Learn how your comment data is processed. Does shpae cone have an edge? Here is a question from to start us off: Parts of a Cone I am a second grade teacher and we are currently teaching a unit on shapes.
The question came up as to whether or not a solid cone has any edges. My contention is that the definition of an edge is where two planes intersect, and therefore a cone cannot how to do cindy lou whos hair an edge.
Another teacher says that the curved surface of a cone represents an infinite number of planes, and therefore represents an infinite number of edges. I would very much appreciate your response, and don't be afraid to w technical. This is as much to satisfy facs own curiosity as to let the kids know the proper answer. The word "edge" is used in different ways; often people get in trouble by introducing the concept of "edge" in the context of polyhedra where it does mean the intersection of two flat facesbut then how to do simplest form about curved surfaces like cones without additional comment.
The other set is called the vertex set; each element of the edge set is determined by a pair of elements of the vertex set In the latter sense which I think is appropriate in discussing a cone, even though the dictionary only mentioned plane figures and not curved surfacesthe cone has one edge. I definitely would not bring in the idea of "an infinite number of edges"; that kind of reasoning generally leads to trouble!
I would simply say that we can extend the concept of edge either from the world of polyhedra definition 2 or from qhat world of plane geometry definition 3 to apply to possibly curved boundaries of possibly curved surfaces, as long as we say that we are doing so. This also agrees with definition 1, which likewise does not require straightness indeed, there is no such concept in graph theoryand which relates to boundaries when we consider planar graphs as in Euler's polyhedral formula.
Coje definition you use depends on what you are going to do with it. If you are just describing objects, my loose definition is fine. If you are going to prove theorems involving planes and angles, you'll want to restrict yourself to the polygonal definition, but then you won't be asking any questions about cones. I think people often fail to realize that even though we are very particular about definitions in math, those definitions may vary from field to field, as they are adapted to a certain context.
That's what I'm trying to do here. The same questions arise concerning faces and vertices, and it's even harder to decide in those cases. Does a cone have a vertex? A year later, we got this question along similar lines: Does a Cone have an Edge? A Vertex? Our 4th grade math textbook defines a cone as "A solid figure with wgat circular face and facee vertex. The textbook defines a face as "A flat surface of a solid. If a cone has only one face, then it whhat possibly have an edge.
Therefore, if it doesn't have an edge, it can't have a vertex. I responded again, after referring faec that previous answer: Elementary texts and high school texts, for that matter are not always very careful about definitions.
The problem really is that the same word can be used with slightly different but related definitions, and we don't always bother to specify how to modify the definitions when we move to a different context. The definitions given are for a polyhedron. When you talk about a cone or cylinder, id have to either use a different set of wordssince "edge" and "vertex" as defined don't apply at all, and "face" applies only to one of the two surfaces of a cone; or you have to modify the definitions to allow curved edges and faces.
Taking the latter approach, the cone will have two faces, one curved, how to do an essay one curved edge. I'm not sure I've ever seen such modified definitions actually stated, but I have no trouble allowing them, as long as love look what you ve done state them clearly!
When they then how to read keyboard sheet music for kids ahead si say it does have an edge or a vertex, children are bound to be confused.
The really tricky part here is that the "vertex" iss a cone has nothing to do with edges, so it needs a whole new definition ; and I can't think of a really good elementary-level definition for what they obviously mean, which is simply a "point.
Does a cylinder have edges? A month later we got yet another question about this, which got a long answer: Number of Cylinder Edges My 8-year-old son was asked "how many edges are there on a solid cylinder? His answer was "2" and it was marked as incorrect. He truly believes in his answer and has asked for my pf in researching.
I answered first, again having referred to the previous answer as background: It depends on how "edge" was defined in his class, which may not agree with his intuitive definition.
Often, an edge is what is foreign direct investments to be straightin which case a cylinder has no edges. Unfortunately, elementary texts are not always very careful about definitions, and they can ask questions like this that are really worthless. The only definition of "edge" that would make sense in this context would be the one your son is naturally using a boundary between smooth surfaces making up an objectwhich would allow a cylinder to have two edges.
Asking this question with the other definition only invites confusion, so I wish they wouldn't ask it. I'd like to hear how they did vone the word. What is the purpose of definitions? But this discussion went further, outside of Ask Dr. I will just quote pieces of it that relate most directly to our present issue of definition: This is a common issue among elementary teachers, and some elementary text book writers.
Basically different sources put down different answers. The underlying issue is: What is the context? What is the larger mathematics one wants to engage with? Without this, there are too many plausible responses. However, some elementary texts and test writers decide they know best and give distinct definitions of 'faces', 'edges', and 'vertices'.
When doing so, there should be some good mathematical reason for doing that. Some set of situations one is trying sshape make sense of. Simple extrapolation on one basis or another, without investigating the good and bad patterns, is a source of trouble. That, unfortunately, routinely happens in elementary and some high school materials. If faces are 'flat regions' and 'edges' are straight linesthen a cylinder has two faces, what is a state resale number edges, and there is no real purpose in the answer.
It does not even help you calculate the surface area! If faces are regions, and edges are where two faces meettbe a cylinder has three faces and two edges no vertices. Thhe still does not seem to be a mathematically interesting description. Some authors even require a face to be a polygon, so that a cylinder has no faces and no edges.
Definitions with no purpose are contrary to the spirit of mathematics, as well as to pedagogy. I suspect that whatever answer this particular test expected, it is based on a particular discussion in a particular text. I can show you different materials with different answers, whatt seldom is there a mathematical discussion. Some people have concluded that, as a ths, it is simply a bad idea distracting without learning to use the words faces, vertices, edges for such objects.
I do not quite agree - but the only really useful context I know is the larger topology, and q can see that this takes a larger understanding, something I only thr at graduate school, and only teach in some upper level undergraduate courses courses most teachers have not taken. Odds are this discussion in wha source text or materials did NOT give enough context to explain why one would bother with these words for this object.
That is where one needs to start. Can a face be curved? Is a curved surface a face or not? Like in a cylinder is the curved surface tge a face? Some people tell me that a curved surface is a face and some say it's not. When I search in Google I also don't get a straight answer. I just want to find out.
I think a curved surface is wjat a face. I took this as a chance to put together a fsce perspective on these questions. As you've discovered, there is no straight answer to this. Facd mathematics, we define terms to meet a need.
What are the Properties of 3D Shapes?
What is Cone? A cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base. This is what a cone looks like: The three main properties of a cone are as follows: It has one circular face. Jun 19, · A cone has a single flat face (also called its base) that's in the shape of a circle. The body of the cone has curved sides that lead up to a narrow point at the top that we call a vertex. A cone contains 1 flat circular face, 1 curved surface, 1 circular edge and 1 vertex. The vertex is formed from the curved surface and it is directly above the centre of the circular base. A cone contains 1 flat circular face on its base. It also has a curved surface wrapping around this curved base.
Asked by Wiki User. If it has one face. A frustum of a cone. A sphere sliced by a plane; or a cone. The answer is - a cone. A Cone. A cone, like an ice cream cone. A cone. A cone? It is a cone. The base is circular and curved, and the tip of the cone is the vertex. Ask Question. Math and Arithmetic. See Answer. Top Answer. Wiki User Answered Related Questions. What shape has 1 vertex 1 face and 1 edge?
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