In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base to a point not contained in the base, called the apex or vertex.
Illustration from Problemata mathematica... published in Acta Eruditorum, 1734
In projective geometry, a cylinder is simply a cone whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.
A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.
In projective geometry, a cylinder is simply a cone whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.
The Tycho Brahe Planetarium in Copenhagen is an example of a truncated cylinder.