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How many edges does a cylinder prism have?

Published in Geometry 2 mins read

The provided question is ambiguous. A "cylinder" and a "prism" are distinct geometric shapes. A cylinder strictly speaking is not a prism. We can address the question by considering a cylinder and a prism separately, and then if the question intended a cylindrical prism, we'll address what that means.

Cylinder

A standard cylinder has two edges. These edges are the circular boundaries at the top and bottom where the curved surface meets the flat circular faces.

Prism

A prism is a polyhedron with two congruent polygonal bases and rectangular lateral faces connecting the bases. The number of edges depends on the shape of the base.

  • Triangular Prism: Has 9 edges.
  • Rectangular Prism: Has 12 edges.
  • Pentagonal Prism: Has 15 edges.
  • Hexagonal Prism: Has 18 edges.

In general, a prism with an n-sided polygon as its base has 3n edges.

Cylindrical Prism

The term "cylindrical prism" is not a standard geometric term. It may refer to a prism whose base is approximated by a polygon that resembles a cylinder as the number of sides of the polygon increases. In the limit, this approaches a cylinder. One could argue that if it were considered a prism, the number of sides would approach infinity, so the number of edges would also approach infinity. However, typically, when considering a shape "in the limit" that approaches a cylinder, we just call it a cylinder.

Therefore, without further clarification, the question is best answered by considering the two shapes separately as above.

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