Why does a cone have one vertex

However, it could be that the question was ambiguous, in which case your son could be correct; we would have to see the question for a definitive response.

In mathematics there are a half dozen different places where the word "vertex" is used, each with a different but similar definition. When you are talking about a cone, a vertex is the point where the straight lines that form the side of the cone meet. Our web site has had many complaints about inconsistent definitions, about vertices in particular.

For an earlier, more complete answer, see mathcentral. That isn't a standard definition. There are several definitions that are standard, each valid in its own context. A vertex of a polyhedron or equivalent shape in other dimensions is a point where edges meet. In two dimensions this would always be two edges; in higher dimensions three or more think of a pyramid. A vertex of a curve is a point where the curvature is higher than anywhere else nearby the ends of an ellipse, for instance.

For a general convex body, a vertex is often defined to be a point at which the intersection of all the supporting hyperplanes there is the point. A hyperplane is a line in the plane, a plane in 3D space, etc. It is "supporting" if it contains the point but no point interior to the body.

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. Look at the sphere.

Ask: Does a sphere have any edges or vertices? This is not a simple question and requires thinking critically about what an edge or vertex is. For example, many real-world objects that we call spheres, such as soccer balls, are in fact complex solid shapes with many edges and vertices. Say: Look at the cone. Ask: Does a cone have any edges?

Again, consider using think-pair-share. Avoid telling students that they are right or wrong. Instead, lead them to see that a cone only has one face, and you need more than one face to form an edge. Ask: Does a cone have any vertices? Lead students to see that a cone has no edges at least no straight ones! Say: Look at the cylinder. Ask: Does a cylinder have any edges or vertices? To explore more attributes of regular solid figures, ask questions such as the following: Which solid figures have opposite faces that are parallel?

For students who are ready, you can ask questions that stretch into higher grade standards and promote a deeper understanding of solid figures: What would the cross-section of a solid look like? How would it change depending on what angle you use? How could you figure out how much liquid it would take to fill up the shape? Be the first to read the latest from Shaped. Subscribe to Shaped. Shaped Staff. October 29, Solid Figure Rectangular Prism.

Number of Faces 6.