want to enhance thins question? Upday ns Inquiry so it'ns on-object for startupcuba.orgematics stack Exchange.

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You are watching: How many faces does a cylinder have

Google is saying 2 and also 3.

What"s the real genuine answer?


the concept that a "face" just applies come polytopes, that is, volumes where every that ns boundary surdeals with are in your area linear. Hence a cube has actually six faces, yet a talking about the deals with that a spbelow ins meaningless. And also ns treatment that the bent border the the cylinder the same, similar thing has nopoint to perform through faces.

If by "face" girlfriend extfinish ns meaning come "any type of maximatogether subset of the boundary such that any 2 pointns in the subsurface can be join through a differentimay be curve lying within ns subsurface" then the cylinder would it is in considered come have $3$ such "faces."

CHoppinns one of ns boundaryns therefore that it have the right to be lhelp flat,k together Google does, ins sort of a cheat, however it will certainly generally offer the exact same result as the extended definition.

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Wbelow ins Google speak the a cylinder has 2 faces? It doesn"t to speak thins in ns screenshot, aldespite it have to Due to the fact that thins is ns Most beneficial prize - as ns following dispute shows.

take it Euler"s formula $F+V=E+2$, consider the number created by drawing a heat dvery own ns cylinder, choose ns seto be top top a tin. Then tbelow to be three faces (two 1-sided round onens and a 3-face cylindricatogether one), two verticens (wbelow ns seto be meets ns height and bottom rim), and also three edge (rim, seam, rim).

If girlfriend remove ns seto be then you reduce the number of edges through 1 through direct deleti~ above and by 2 by merger Since a vertex is rerelocated (an leaf goes indigenous crest come vertex: no vertex means no edge), ns variety of vertices by 2, and friend unify ns cylindricatogether faces by rerelocating the seam, thus reducing your number therefore that insteAD of 1 that lock friend have 0 the them. Therefore $F+V=2+0=0+2=E+2$.

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ns intuiti have justificatitop top for this way the countinns ins the an $n$-gtop top is surrounded by $n$ linens (a 1-gtop top is surrounded by 1 line) however ns cylindrical challenge is no surrounding in ~ every - friend can go along ins for ever and also ever and also never before hins a boundary. This unusual character is fittingly recognised through calling it a $0$-gon.

Google"s quoted discussion ins defecti have Because it counts the deals with no that a cylinder yet of a cylinder pluns a seam: a various number altogether.