What is the vertex at the top of a cone or a pyramid called?

The correct term for the vertex at the top of a cone or a pyramid is "apex." This term specifically refers to the highest point of these three-dimensional shapes. In geometry, the apex is used to describe the common point where the sides or lateral edges meet. It is important to distinguish this term from others that might seem similar, such as "peak," "summit," or "pinnacle," which are more general terms and may refer to the highest point of various objects, but are not specifically defined in geometric vocabulary for cones and pyramids. Thus, "apex" is the precise and accurate term used in mathematical contexts.