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The axis of a cone is the straight line passing through the apex about which the cone has a circular symmetry. In common usage in elementary geometry, cones are assumed to be right circular, i.e., with a circle base perpendicular to the axis. [1] If the cone is right circular the intersection of a plane with the lateral surface is a conic section.
The bare term cylinder often refers to a solid cylinder with circular ends perpendicular to the axis, that is, a right circular cylinder, as shown in the figure. The cylindrical surface without the ends is called an open cylinder. The formulae for the surface area and the volume of a right circular cylinder have been known from early antiquity.