Why does a cone have 1 vertex

He truly believes in his answer and has asked for my assistance 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 required to be straight , in 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 object , which 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 define 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 to 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 lines , then a cylinder has two faces, no 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 meet , then a cylinder has three faces and two edges no vertices.

This 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, but seldom is there a mathematical discussion.

Some people have concluded that, as a result, 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 you can see that this takes a larger understanding, something I only learned at graduate school, and only teach in some upper level undergraduate courses courses most teachers have not taken.

Notify me of new posts by email. Skip to content. How many vertices does a cone have? Other 3D Shapes — Flat Surface and Vertices count As a point of reference the following shapes have the corresponding amount of vertices A cube had 6 flat surfaces and 8 vertices A cone has 1 flat surface the circle at the top and technically 1 vertex A rectangular prism has 6 flat surfaces and 8 vertices A cylinder has 3 flat surfaces and no vertex The cylinder is the only shape out of those listed we were able to prove categorically that it has no vertex.

Picture Guide for Shapes and their Vertices Also, I am sharing a picture guide that depicts the various shapes with the corresponding amount of vertices, faces and edges. Share:- Twitter Facebook Pinterest Print. Because so much of this lesson relies on examining and analyzing physical objects, it works well for students who are visually impaired. In place of the table below, explain what information you are looking for and have students describe the same information for each of the solid figures.

Ask: How many faces does a rectangular prism have? Say: The line segment where two faces meet is an edge. Hold up a solid figure and show students an example of an edge. Count the number of edges a rectangular prism has. Mark each edge as you count. Similar to faces, use a marker, stickers, or sticky notes. Ask: How many edges does a rectangular prism have? Say: The point where edges meet is a vertex. Count the number of vertices a rectangular prism has.

Mark each vertex as you count. Ask: How many vertices does a rectangular prism have? Have students find the number of faces, edges, and vertices of a cube and a pyramid. Record the answers in the table. Ask: Why do you think that a rectangular prism and a cube have the same number of faces, edges, and vertices?

Lead students to realize that the faces of a rectangular prism and a cube are all rectangles, but in the case of the cube, the rectangles are squares. A cube is a special type of rectangular prism. I have found this to be an interesting topic to navigate and appreciate the information.

Like Like. You are commenting using your WordPress. You are commenting using your Google account. You are commenting using your Twitter account. You are commenting using your Facebook account. Notify me of new comments via email. Notify me of new posts via email. Email Address:. Blog at WordPress. Take a look at this picture of a rectangular prism : How many vertices does it have? Take a look at this picture of a cone : How many vertices does it have? Does the point at the top count?

Source: Plane and Solid Geometry , George Wentworth, , pages and It is important for students to see a variety of examples of two- and three-dimensional figures. Math : What definition you use depends on what you are going to do with it.

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