Cones

A cone is a solid formed by joining the points of a plane base to an apex outside that plane. A circular cone has a circular base.

Circular Cones

A right circular cone has its apex directly above the centre of its circular base. Its axis is perpendicular to the base; in an oblique circular cone it is not.

Right Circular Cone

A right circular cone can be visualised as the limiting shape of right regular pyramids whose bases approach a circle as their number of sides increases.

A cone is not a pyramid: a pyramid has a polygonal base with finitely many straight edges, whereas a circle is not a polygon. The sequence of pyramids illustrates a limiting relationship.

Like the volume of a pyramid, the volume of the cone is also \(\frac{1}{3}\times \) base area \(\times \) height. Since the base area of a circular cone is \(\pi {{r}^{2}}\), thus the volume of cone will be:

Volume of cone = \(\frac{1}{3}\times \) base area \(\times \) height = \(\frac{1}{3}\times \) \(\pi {{r}^{2}}\) \(\times \) \(h\)

In the syllabus, we often refer the right circular cone as cone.