Question

How come a three-dimensional figure with a curved surface is not a polyhedron?

Answer 1

Hint: We should know the difference between a two-dimensional figure and a three-dimensional figure. Also, a three-dimensional figure can have both curved surfaces and plane surfaces. A cylinder cannot be a polyhedron because it has a curved surface and no plane surface.

Complete step-by-step solution:
A three-dimensional figure is a figure that has curved surfaces in it and it also includes pyramids and prisms. Also, a three-dimensional figure has thickness and depth too.
The basic three-dimensional shapes that we see around us include a cube, rectangular prism, sphere cone, and cylinder.
The three-dimensional shape that we see around us in our day to day life includes, we can see a rectangular prism in our school notebook, we can see the shape of a sphere in a ball, a shape of a cone can be seen in a carrot, the shape of a cylinder can be seen in the form of the bucket.
On the other hand, a polyhedron is a three-dimensional figure that has plane surfaces in it; straight edges and vertices are also present there. A cube, a prism, and pyramids are the three-dimensional surfaces that are polyhedrons.
Faces, edges, and vertices are considered as the dimensions of the polyhedron. The flat surfaces in the polyhedron are considered as the faces of the polyhedron. Edges in the polyhedron are where the two surfaces of the polyhedron meet each other and the point of intersection of two edges in the polyhedron is known as the vertices of the polyhedron.
There is a formula that represents the relationship between the vertices, edges, and faces of the polyhedron are represented as Euler’s formula which is given by,
\[F+V-E=2\]
where F is the face, V is the vertices and E is the edges.
So from above, it can be seen that a three-dimensional shape with curved surfaces cannot be a polyhedron because, in a polyhedron, flat surfaces are present and not curved surfaces.

Note: Shapes can also be considered as two-dimensional surfaces two in which only height and weight are present only and depth is not present. Every structure in the universe is only considered as a three-dimensional surface but not a two-dimensional surface. Circle, square, and rectangle are all examples of two-dimensional surfaces.