Faces located in a cylinder

Unlike the faces of polyhedra, not all cyndrical tube faces are planar surface areas. Cyndrical tubes are comprised of 3 faces, 2 round faces that develop the bases of the cyndrical tube as well as one face created by the remainder of the surface area of the cyndrical tube. If we expanded the cyndrical tube, the 3rd face would certainly have the form of a rectangular shape as received the representation:

diagram of the surface area of a cylinder

If we include the locations of the 3 faces, we will certainly acquire the surface of the cyndrical tube. We understand that each round face should have a location of πr ², so both bases have a location of 2πr ² . The 3rd face is created by extending the surface area that signs up with the bases.

By extending this surface area, we develop a rectangular shape that has a size equivalent to the area of the round bases as well as an elevation equivalent to the elevation of the cyndrical tube. For that reason, the location of this surface area is 2πrh. The complete surface amounts to 2πr ² + 2πrh.


Vertices located in a cylinder

In the instance of polyhedra, vertices are the factors where 2 line sections satisfy. For cyndrical tubes, we are taking into consideration the CW facility framework, as stated in the intro. This permits us to take into consideration encounters that have rounded surface areas as well as sides that likewise have curvature.

Therefore, we can end that we have 2 vertices in a cyndrical tube, one in each circle. We can analyze this as the factor we note when we start to map a circle as well as where we end up a total turn.

In enhancement, we can likewise take into consideration those factors, as the locations where the rounded surface area of the cyndrical tube is signed up with.

vertices of a cylinder

Sides located in a cylinder

The sides are taken into consideration as line sections at the restrictions of polyhedra that sign up with 2 vertices. Nevertheless, in cyndrical tubes, we have 2 sides that have curvature, which are the areas of the circles at the bases.

In enhancement, we have a 3rd side that signs up with both vertices of the circles which lies along the side face. For that reason, we have an overall of 3 sides.

edges of a cylinder

We have actually seen that a cyndrical tube has 3 faces, 2 vertices, as well as 3 sides. This adheres to the Euler characteristic, which is a certain number that permits us to define the form or framework of polyhedra or topological areas.

Therefore, the Euler quality of a cyndrical tube is 2-3 + 3 = 2, which concurs with the Euler quality of 2 of a ball. This is appropriate because a cyndrical tube is homotopically comparable to a ball.


See also

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