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 Math Central Quandaries & Queries
 Subject: flat surfaces, vertices, and edges Name: Stacy Who are you: Parent A cylinder has how many flat surfaces, vertices, and edges?

Hi,

A cylinder has 3 faces - 2 circle ones and a rectangle (if you take the top and bottom off a tin can then cut the cylinder part on the seam and flatten it out you would get a rectangle). It has 2 edges and no vertices (no corners).

Diane

Hi Stacy,

I really like your question because it makes me think about the way we use words in everyday conversation and in the technical mathematical sense. Diane sees a cylinder as a "soup can" which is how I think most people in everyday language would use the word. She also says there are three faces because the top and bottom are each a face and "if you take the top and bottom off a tin can then cut the cylinder part on the seam and flatten it out you would get a rectangle". I agree with Diane that with this meaning of the word cylinder it has 3 faces, 2 edges and no vertices.

There is however a technical meaning of the word cylinder that results in a different answer. The technical name for the cylinder Diane describes is a right, circular cylinder. Circular since the cross section is a circle rather than some other shape and right because it stands up straight rather than leaning over like the Tower of Pisa. Also a right circular cylinder doesn't have a top or bottom, the circular side extends infinitely up and down. With this understanding of the word cylinder it has one face, no edges and no vertices.

Penny

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