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What sort of pyramid has a circle base?
A cone
What happens to the shape of a pyramid as the number of faces increases?
It depends on whether or not the pyramid base remains convex or if whether some of the additional sides created ridges. If the base remains convex, sections of the pyramid base will become more like a circle and the sloped surface above that part will become smoother. It would be wrong to conclude that the pyramid would become more like a cone because it is entirely possible that all the additional sides - possibly infinitely many - are all between two adjacent vertices of the original base polygon. You would then have a base that is a segment of a circle - a third, or a quadrant, etc..
How are a cone and a pyramid alike?
Start with a regular tetrahedron (triangular based pyramid). As you increase the number of sides in the base of the pyramid, the shape becomes more and more like a right cone. In the limit, the base tends to a polygon with an infinite number of sides - a circle, and the pyramid tends to a right cone.
How is a pyramid like a cone?
A cone is a pyramid in its limit - when the base has infinitely many vertices.
Is it true that a cone is actually circle based pyramid?
Yes, it is a pyramid and a circle on the bottom
