Although Euler's Theorem does not apply when describing the attributes of the nets of cylinders and cones, there are some special relationships.  However, these relationships will become more apparent once you begin to use nets in the application of measuring solids.

The image on the left shows a rectangle on its side with 2 circles attached to the top and bottom.  The image on the right shows a circle with a sector attached below it.

Interactive exercise. Assistance may be required. Study the nets for a cylinder and a cone shown above. Use the diagrams to determine the appropriate word for each blank describing the attribute of each net. Use the dropdown menus to select the appropriate word.


Pause and Reflect

An edge is the intersection of two or more faces, and a vertex is the intersection of two or more edges. Do cylinders or cones have edges and vertices? How do you know?

Interactive popup. Assistance may be required.

Check Your Answer

No. Because none of the surfaces of cylinders or cones are polygons, they cannot be faces. Since there are no faces, there cannot be edges. Since there are no edges, there cannot be vertices. Close Pop Up

The peak of a cone is sometimes called an apex or a vertex of the cone. How is this vertex like vertices in polyhedra? How is it different?

Interactive popup. Assistance may be required.

Check Your Answer

The vertex of a cone is like a vertex of a polyhedron in that it is a point along the outside of the three-dimensional figure. It is different because there are no defined edges that intersect to create the vertex. In fact, it appears as though there are an infinite number of edges that intersect to create the vertex of a cone. Close Pop Up