Question

Explain why a three-dimensional figure with a curved surface is not a polyhedron.

Answer 1

Polyhedron, by definition, is formed by intersecting planes, so each part of its surface is either a vertex or an edge, or a flat piece of a plane.

Answer 2

We are given a '3-D figure with a curved surface'.

Now, we know that,

Polyhedron is a three dimensional figure having polygon faces.

Which means that the faces of the polyhedron are 2-D closed shapes bounded by straight lines.

Since, the 3-D figure consists of curved surface and the polyhedron does not have any curved surface.

Thus, we have,

A three-dimensional figure with a curved surface is not a polyhedron.