Definition:Cylinder
Definition
A cylinder is a solid figure formed by cutting a cylindrical surface by $2$ parallel planes at an angle greater than $0$ to the generatrices.
Base of Cylinder
The $2$ parallel planes which form a cylinder by intersecting a cylindrical surface are called the bases.
In the above diagram, the bases of the cylinder $ACBEDF$ are the faces $ABC$ and $DEF$.
Lateral Surface of Cylinder
The lateral surface of a cylinder is the curved surface between the bases.
Slant Height of Cylinder
The slant height of a cylinder is the length of a generatrix.
In the above diagram, $s$ is the slant height of the cylinder $ACBDFE$.
Height of Cylinder
The height of a cylinder is the length of a line segment drawn perpendicular to the base and its opposite plane.
In the above diagram, $h$ is the height of the cylinder $ACBDFE$.
Similar Cylinders
Let $h_1$ and $h_2$ be the heights of two cylinders.
Let $d_1$ and $d_2$ be the diameters of the bases of the two cylinders.
Then the two cylinders are similar if and only if:
- $\dfrac {h_1} {h_2} = \dfrac {d_1} {d_2}$
In the words of Euclid:
- Similar cones and cylinders are those in which the axes and the diameters of the bases are proportional.
(The Elements: Book $\text{XI}$: Definition $24$)
Also see
- Results about cylinders can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cylinder
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cylinder