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Chapter 10: Problem 50

Explain why a cylinder is not a polyhedron.

Short Answer

Expert verified
A cylinder is not a polyhedron because it does not fulfill the criteria of a polyhedron. It has a curved surface, while a polyhedron only consists of flat faces and straight edges.

Step by step solution

01

Understanding a Polyhedron

A polyhedron is a three-dimensional geometric figure that has flat faces and straight edges. Specifically, a polyhedron is a solid bounded by polygons, such that each edge is shared by exactly two faces.
02

Understanding a Cylinder

A cylinder is a three-dimensional figure with two parallel, congruent circular bases that are connected by a curved surface. The curved surface is formed by all the lines from each point on the boundary of one base to the corresponding point on the boundary of the other base. This curved surface is called a curved face.
03

Comparing a Cylinder and a Polyhedron

In comparison with a polyhedron, a cylinder does not have all flat faces and its edges are not all straight lines. Specifically, it has a curvature on its lateral surface between the two bases. This disqualifies it from being a polyhedron. A polyhedron cannot have a curved surface.

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