Definition:Cylinder

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Definition

Cylinder.png

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