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Home
Maths
Cylinder

Cylinder

The word "cylinder" is derived from the Greek word "Kylindros," meaning "roll" or "roller." A cylinder is a three-dimensional figure that is made up of a curved surface, a circular top, and a circular bottom. It is one of the most basic curvilinear geometric shapes that has both mathematical and real-world applications. Toilet paper rolls, cold drink cans, and pipes are a few of the basic examples of the cylinder shape in real-life situations. In this blog, we will explore different types of cylinders and essential formulas like surface area (CSA and TSA of cylinder) and volume of a cylinder.

1.0Key Properties of a Cylinder

Every geometrical shape has its own unique characteristics, and a cylinder is no different. Let’s look at some of the key properties of a cylinder:

  • Every cylinder is made up of a curved surface and two flat faces, which are identical.
  • A cylinder does not have any verticals like a cone, cube, or cuboid. 
  • The two circular bases are always congruent and parallel. 
  • The size of a cylinder is determined by the height and radius of the base.
  • A cylinder has the same base and the same top, whether it is circular or elliptical.

2.0Types of Cylinders

Cylinders come in different types based on the cylindrical shapes and orientation. There are five types of cylinders, which are right circular cylinders, half-cylinders, elliptical cylinders, hollow cylinders, and horizontal cylinders. Refer to the below table to understand the different types of cylinders in detail. 

Type of Cylinder

Description

Example

Diagram

Right-Circular Cylinder

Also known as the right cylinder, this is characterised by perpendicular lines connecting the centres of the circular bases. 

Soda cans, storage tanks.


Half Cylinder

A half cylinder is created when a cylinder is truncated longitudinally or, in easier words, lengthwise cut in half. 

Semi-circular drainage pipes.


Elliptical Cylinder

An elliptical cylinder is a three-dimensional geometric shape with an elliptical cross-section. It means when you cut the cylinder perpendicular to the length, the shape of the cut is an oval rather than a circle.

Aircraft fuselages, fuel tanks.


Hollow Cylinder

A hollow cylinder is when a cylinder that is empty has some difference between the internal and external radius. 

Water pipes, tunnels.


Horizontal Cylinder

A horizontal cylinder refers to a cylindrical shape that is positioned in a way so the axis is parallel to the ground.

Fuel tanks, pipelines.


3.0Surface Area of a Cylinder (CSA and TSA of Cylinder)

The surface area of an object refers to the total area occupied by the said object. The cylinder is a common three-dimensional geometric shape. Because of its three-dimensional nature, one needs to calculate the curved surface area and the total surface area, known as the CSA and TSA of Cylinder. 

  • Curved Surface Area (CSA) of a Cylinder

The curved surface area refers to the area of only the curved surface, leaving the circular top and the base. If the height of a cylinder is seen as “h” and the base radius as "r,” then the curved surface area of a cylinder would be:

C.S.A= 2πrh 

Example: Find the curved surface area of a cylinder with a radius of 14 cm and a height of 21 cm.

Solution: 

CSA=2πrh

Now the value of r=14 cm (radius), h=21 cm (height), and π≈3.1416

Now, substituting the values:

CSA = 2 × 3.1416 × 14 × 21

CSA =2 × 3.1416 × 294

CSA = 1847.52 cm²

So, the curved surface area of the cylinder is 1847.52 cm².

  • Total Surface Area (TSA) of a Cylinder

The total surface area of a cylinder includes the area of the surface as well as the two circular bases. If the cylinder has the base radius "r” and the height is denoted by “h,” then the total surface area of a cylinder is the sum of the curved areas and the circular areas of the cylinder. 

TSA = 2πr(r + h)

Example: Find the total surface area of a cylinder having a radius equal to 5 cm & height 8 cm.

Solution: 

The total surface area (abbreviated as TSA) of a cylinder may be calculated using the formula TSA = 2πr(r + h).

By substituting the values of radius (r) = 5, height (h) = 8, we get:

TSA = 2πr2+2πrh = 2πr(r+h) = 2 × 3.14 × 5(5 + 8) = 408.41 cm².

4.0Volume of a Cylinder

The volume of a cylinder refers to the amount of space the cylinder can hold. To calculate the volume of a solid cylinder, one needs to multiply the base area of the cylinder by its height. 

Volume: π r² h

Example: A cylinder has a radius equal to 50 cm and a height equal to 100 cm. How to find the volume of a cylinder?

Solution:

As we know, the volume of a cylinder is given by the formula – π r2 h, where

r is its radius = 50 cm and

h is the height = 100cm.

Therefore, putting the values we get, 

V = π r² h

V = 3.14 x 502 x 100 

V = 785,000 cm³

5.0Conclusion

By understanding the cylinder and its mathematical applications, you can apply them in real-world situations and significantly benefit from it. Students are advised to practise questions based on CSA and TSA of Cylinder as well as how to calculate the Volume of a Cylinder to ace their examinations.

Table of Contents


  • 1.0Key Properties of a Cylinder
  • 2.0Types of Cylinders
  • 3.0Surface Area of a Cylinder (CSA and TSA of Cylinder)
  • 3.1Curved Surface Area (CSA) of a Cylinder
  • 3.2Total Surface Area (TSA) of a Cylinder
  • 4.0Volume of a Cylinder
  • 5.0Conclusion

Frequently Asked Questions

There are five types of cylinders: right circular cylinders, half-cylinders, elliptical cylinders, hollow cylinders, and horizontal cylinders.

The CSA and TSA of a cylinder can be easily calculated using mathematical formulas. The CSA, or the curved surface area of a cylinder, is 2πrh. The TSA of the total surface area of a cylinder is 2πr(r + h).

To calculate the volume of a cylinder, one needs to use the formula π r² h, where “r” is the radius of the circular base and “h” is the height.

Some examples of cylindrical shapes would be gas tanks and soda cans.

The most noticeable properties of a cylinder include it is made up of a curved surface and two flat faces, which are identical. These do not have any verticals. The size of a cylinder is determined by the height and radius of the base.

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