Cylinder

A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis. The perpendicular distance between the bases is the height, “h” and the distance from the axis to the outer surface is the radius “r” of the cylinder.

Properties of a Cylinder

There are so many properties that make a cylinder unique. Some of them are:

  • A cylinder has no vertex.
  • The curved surface of a cylinder is actually just a folded rectangle.
  • The top and base of a cylinder can actually be varied to produce different types of cylinders.
  • The bases are always congruent and parallel.
  • If the axis forms a right angle with the bases, which are exactly over each other, then it is called a “Right Cylinder”.
  • It is similar to the prism since it has the same cross-section everywhere.
  • If the bases are not exactly over each other but sideways, and the axis does not produce the right angle to the bases, then it is called “Oblique Cylinder”.
  • If the bases are circular in shape, then it is called a right circular cylinder.
  • If the bases are in an elliptical shape, then it is called an “Elliptical Cylinder”.

If the axis of the cylinder is a straight vertical line, or the cylinder stands totally upright with two identical circular bases, it is called a right circular cylinder.

A right and an oblique circular cylinder

Surface area

Having radius r and altitude (height) h, the surface area of a right circular cylinder, oriented so that its axis is vertical, consists of three parts:

  • the area of the top base: πr2
  • the area of the bottom base: πr2
  • the area of the side: rh

Curved Surface Area : The curved surface area of a cylinder can simply be defined as the area of the rolling part of the cylinder, i.e., the area of the curved part. 

The formula for the curved surface area of the cylinder is given as  2 ✕ π✕ r ✕ h

Total Surface Area : The total surface area of a cylinder is the sum of its curved surface area and the sum of the areas of its two bases:

Total surface area = Curved surface area + 2 ✕ area of circular base

                               =2π r h + 2 ✕π r =2 πr( h + r)

Volume of a Cylinder : The volume of a cylinder is defined as the amount of space it has that can be filled. 

The volume of a cylinder is given by the formula:  π ✕ r2 ✕ h.