Definition:Cylinder

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Definition

Cylinder.png

A cylinder is a solid made by rotating a rectangle along one of its sides.


In the words of Euclid:

When, one side of those about the right angle in a rectangular parallelogram remaining fixed, the parallelogram is carried round and restored again to the same position from which it began to be moved, the figure so comprehended is a cylinder.

(The Elements: Book $\text{XI}$: Definition $21$)


In the above diagram, the rectangle $ADHG$ has been rotated around the side $GH$ to produce the cylinder $ACBEFD$.


Axis of Cylinder

In the words of Euclid:

The axis of the cylinder is the straight line which remains fixed and about which the parallelogram is turned.

(The Elements: Book $\text{XI}$: Definition $22$)


In the above diagram, the axis of the cylinder $ACBEFD$ is the straight line $GH$.


Base of Cylinder

In the words of Euclid:

And the bases are the circles described by the two sides opposite to one another which are carried round.

(The Elements: Book $\text{XI}$: Definition $23$)


In the above diagram, the bases of the cylinder $ACBEDF$ are the faces $ABC$ and $DEF$.


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 $24$)