Vertices of a Cone

A cone is a three-dimensional geometric shape that has a circular base and a pointed top called the apex. The number of vertices of a cone is an important characteristic of this shape.

Definition of a Vertex:
A vertex is a point where two or more edges or lines intersect in a geometric shape. In other words, it is a corner or a meeting point of edges.

Understanding a Cone:
A cone has two main components: the circular base and the apex. The circular base is a flat surface in the shape of a circle, while the apex is the topmost point of the cone. The base and the apex are connected by curved surfaces, forming the lateral surface of the cone.

Number of Vertices in a Cone:
A cone has only one vertex, which is the apex. The apex is the only point where the edges of the cone intersect. There are no other corners or meeting points of edges in a cone.

Explanation:
To understand why a cone has only one vertex, we can visualize the shape of a cone and examine its properties:

1. Base: The base of a cone is a circle. A circle does not have any vertices because it is a curved shape with no corners or meeting points of edges.

2. Lateral Surface: The curved surface connecting the base to the apex is also smooth and continuous. It does not have any sharp corners or intersections.

3. Apex: The apex of a cone is a single point. It is the topmost point where all the edges of the cone converge.

Since there are no corners or meeting points of edges on the base or the lateral surface, the only vertex in a cone is the apex.

Conclusion:
In conclusion, a cone has one vertex, which is the apex. The base and the lateral surface of a cone do not have any vertices. Therefore, the correct answer to the question is option 'C' - 1.