Cylinder
A cylinder is a closed solid that has two parallel (usually circular) bases connected by a curved surface.
Try this
In the figure below, drag the orange dot to vary the dimensions of the cylinder.
Base and side
A cylinder is a geometric solid that is very common in everyday life, such as a soup can.
If you take it apart you find it has two ends, called
bases,
that are usually circular.
The bases are always
congruent
and
parallel
to each other.
If you were to 'unroll' the cylinder you would find the the side is actually a rectangle when flattened out.
(See Surface area of a cylinder).
Height
The height h is the perpendicular distance between the bases. It is important to use the perpendicular height (or 'altitude') when calculating the volume of an oblique cylinder.
Radius
The radius r of a cylinder is the
radius
of a base. If you are given the diameter instead, remember to halve it.
Axis
A line joining the center of each base.
Right and oblique cylinders
When the two bases are exactly over each other and the axis is a right angles to the base, this is a called a 'right cylinder'.
If one base is displaced sideways, the axis is not at right angles to the bases and the result is called an oblique cylinder.
The bases, although not directly over each other, are still parallel.
In the applet at the top of the page, check the "allow oblique" box and drag the orange dot sideways to see an oblique cylinder.


Right Cylinder 
Oblique Cylinder 
Volume and surface area
The shape of the bases
Usually the bases are circles, so a familiar soup can would be technically called a 'right circular cylinder'.
This is the most common kind, and if someone just says 'cylinder' this is usually what they mean.
The bases can however be almost any curved shape, but the most common alternative to a circle is an
ellipse. The shape would then be called an 'elliptical cylinder'.
Relation to a prism
A prism is a solid with bases that are polygons and the sides are flat surfaces.
(See Definition of a prism). Strictly speaking a cylinder is not a prism, however it is extremely similar.
In a prism where the bases are regular polygons, the prism begins to approach being a cylinder when the number of sides is large.
For more on this, see Relation of a cylinder to a prism.
Another way to produce a cylinder
Another way to produce a circular cylinder is to consider it the
locus
of a line moving parallel to, and a fixed distance from the axis.
For more on this see Cylinder as the locus of a line.
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