Right circular cylinder

Thus, in a right circular cylinder, the generatrix and the height have the same measurements.

[1] It is also less often called a cylinder of revolution, because it can be obtained by rotating a rectangle of sides

[2] In addition to the right circular cylinder, within the study of spatial geometry there is also the oblique circular cylinder, characterized by not having the geratrices perpendicular to the bases.

[2] The lateral surface of a right cylinder is the meeting of the generatrices.

[3] It can be obtained by the product between the length of the circumference of the base and the height of the cylinder.

, we have: or even Through Cavalieri's principle, which defines that if two solids of the same height, with congruent base areas, are positioned on the same plane, such that any other plane parallel to this plane sections both solids, determining from this section two polygons with the same area,[6] then the volume of the two solids will be the same, we can determine the volume of the cylinder.

[4] Then, assuming that the radius of the base of an equilateral cylinder is

[4] Its lateral area can be obtained by replacing the height value by

: The result can be obtained in a similar way for the total area: For the equilateral cylinder it is possible to obtain a simpler formula to calculate the volume.

Simply substitute the radius and height measurements defined earlier into the volume formula for a straight circular cylinder: It is the intersection between a plane containing the axis of the cylinder and the cylinder.

[4] In the case of the right circular cylinder, the meridian section is a rectangle, because the generatrix is perpendicular to the base.

The equilateral cylinder, on the other hand, has a square meridian section because its height is congruent to the diameter of the base.