Introduction

The cylinder is a unique shape that is three-dimensional and it consists of two circular bases which are parallelly positioned to each other and one curved surface that joins the two circular bases at a specific distance from the center. As cylinders are three-dimensional (3D), it has a definite area and volume. Real-life examples of cylinders are jars, toilet paper rolls, cans, fire extinguishers, etc. if all the parts of a cylinder are to be seen separately, it will be evident that this shape is formed as a result of the combination of two circles (the two bases) and one rectangle (the middle portion will form the shape of a rectangle if the curved structure is flattened and straightened out). 

Parts Of a Cylinder

Other than the two bases and one rectangular body, any cylinder will consist of all the following parts; 

  1. Radius- The distance between the center to any side of any of the two bases will be the radius of the cylinder. 
  2. Height- The total distance between the two parallel bases is recognized as the height or perpendicular distance of the cylinder and represented as ‘h’. 
  3. Axis- The axis is the central line passing through the body (height) of the cylinder and joining the two bases. 

Cylinder Formulae

Related to the area and volume, the cylinder shape has three main formulae. They are lateral surface areas also known as curved surface area, total surface area, and cylinder volume.

  1. Curved Surface Area of Cylinder (CSA)- Curved or lateral surface area represents the curved area between the two circular bases. The formula to find out this specific area of the cylinder is:

Curved Surface Area (CSA)= Circumference × height

= 2πrh square units. (Where r is radius and ‘h’ is height and π value is considered as 22/7 or 3.14 approximately). 

  1. Total Surface Area (TSA)- The Total Surface Area (TSA) will include all the areas of the cylinder i.e., the lateral surface and the two circular bases as well. Thus, before finding out the TSA, the CSA of both the circles is required. 

Firstly, CSA= Circumference × height= (2πr × h)

We know, Area of the circle: πr²

Therefore, to calculate the Total Surface Area (TSA) of the cylinder, we have to use this formula: 

Total Surface Area (TSA)= Curved Surface Area + 2(Area of a circle)

Therefore, 

TSA= 2πrh + 2πr² = 2πr (h + r) square units. (Where r is radius and h is the height).

Note: As there are two circles in the cylinder, the area of the base which is the circle is simply multiplied by 2).

  1. Cylinder Volume- This cylinder volume formula figures out the total density or the total space the cylinder is occupying. In other words, suppose a cylinder is to be filled with water, then the total amount of water that will be required to fill the whole cylinder will be equivalent to the cylinder’s volume. The formula can be calculated by; 

Volume (V) = Area of the circle × height

= πr² × h (Here, r is radius and h is the height)

Therefore, the volume will be πr²h cubic units.

Conclusion

The cylinder is a shape that is 3-D in nature and consists of two circular bases and one curved rectangular surface between the two bases. Unlike other shapes such as cones, cuboids, or cubes, a cylinder does not have any corner or vertex. The size of any cylinder will depend on the radius of the base and both the bases will always be equal.