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You are watching: How many faces on a cylinder

Google is saying 2 and also 3.

What"s the actual real answer?

The notion of a "face" only applies to polytopes, that is, quantities where each of the boundary surfaces are locally linear. For this reason a cube has actually six faces, but a talking about the deals with of a sphere is meaningless. And the treatment of the curved border of the cylinder an in similar way has nothing to perform with faces.

If by "face" you extend the meaning to "any maximal subset the the border such that any type of two points in the subsurface deserve to be joined by a differentiable curve lying within the subsurface" then the cylinder would certainly be thought about to have $3$ such "faces."

CHopping one of the boundarys so the it have the right to be laid flat,k together Google does, is sort of a cheat, but it will usually give the same result as that expanded definition.

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answer Jul 19 "16 at 20:42

mark FischlerMark Fischler

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Where is Google saying the a cylinder has 2 faces? it doesn"t speak this in the screenshot, although that should due to the fact that this is the most useful answer - together the following argument shows.

Take Euler"s formula $F+V=E+2$, think about the figure produced by illustration a line down the cylinder, prefer the seam on a tin. Then there are three deals with (two 1-sided ring ones and one 3-sided cylindrical one), two vertices (where the seam meets the top and also bottom rim), and also three edge (rim, seam, rim).

If you remove the seam climate you minimize the variety of edges by 1 by straight deletion and by 2 through merging because a crest is gotten rid of (an edge goes indigenous vertex to vertex: no vertex means no edge), the number of vertices by 2, and you merge the cylindrical deals with by removing the seam, thus reducing your number for this reason that instead of 1 of them you have actually 0 of them. Hence $F+V=2+0=0+2=E+2$.

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The intuitive justification for this means of counting is the an $n$-gon is surrounded by $n$ present (a 1-gon is surrounded by 1 line) yet the cylindrical face is no surrounded at every - you have the right to go follow me it because that ever and also ever and never hit a boundary. This unexplained character is fittingly recognised by calling it a $0$-gon.

Google"s quoted dispute is defective since it counts the faces not that a cylinder but of a cylinder add to a seam: a different figure altogether.