Cylinder
A cylinder is a three-dimensional solid figure which has two identical circular bases joined by a curved surface at a particular distance from the center which is the height of the cylinder. Toilet paper rolls, cold drink cans are real-life examples of cylinders. Also, do you know that the Leaning Tower of Pisa is cylindrical in shape?
The word "cylinder" is derived from the Greek word "kylindros" meaning "roll" or "roller." The term was first used in mathematics to describe the geometric shape of a solid figure with a circular base and straight sides, and was later applied to other cylindrical objects such as pipes, containers, and engine parts. Let us learn more about cylinder shape in this article.
| 1. | Definition of Cylinder |
| 2. | Cylinder Faces Vertices Edges |
| 3. | Types of Cylinder |
| 4. | Properties of Cylinder |
| 5. | Formulas of Cylinder |
| 6. | FAQs on Cylinder |
Cylinder Definition
A cylinder is a 3D solid shape that consists of two identical and parallel bases linked by a curved surface. These bases are like circular disks. The line passing from the center or joining the centers of two circular bases is called the axis of the cylinder shape. The distance between the two bases is called perpendicular distance and is represented as height, “h”. The two circular bases have a distance from the center to the outer boundary which is known as the radius of the cylinder, represented by “r”. The cylinder is a combination of 2 circles + 1 rectangle.
Look at the given image showing the formation of the cylinder shape.
Some real-life examples of cylinder shape are pipes, fire extinguishers, water tanks, cold-drink cans, etc.
Cylinder Faces Vertices Edges
A cylinder has two circular faces and one curved surface. The circular faces are congruent (equal in size and shape) and are located at each end of the cylinder. The curved surface connects the two circular faces and is shaped like a rectangle that has been rolled up into a tube. Let us see how many faces, vertices, and edges a cylinder has:
- Faces: A cylinder has 3 faces in total (2 flat circular faces + 1 curved face)
- Edges: A cylinder has 2 edges (one at the top and one at the bottom)
- Vertices: A cylinder has 0 vertices (as the two edges of cylinder never meet anywhere)
Types of Cylinder
We just read about some real-life examples of a cylinder, which shows that it can be of various types. In geometry, there are four different types of cylinders. They are as follows:
- Right Circular Cylinder: If the axis of the two parallel bases is perpendicular to the center of the base, it is called the right circular cylinder. Example: soda can.
- Oblique Cylinder: An oblique cylinder is one whose sides lean over the base. In this, the sides are not perpendicular to the center of the base. Example: The Leaning Tower of Pisa.
- Elliptic Cylinder: A cylinder whose base is in the form of an ellipse is called an elliptic cylinder. Example: optical lens.
- Right Circular Hollow Cylinder or Cylindrical Shell: It consists of two right circular cylinders bounded one inside the other. The point of the axis is common and is perpendicular to the central base. It is different from the right circular cylinder since it is hollow in nature, i.e. there is some space or void present inside. Example: Hydraulic Cylinders.
Look at the image below to get an overview of all four types of cylinders explained above.
Properties of Cylinder
Every geometrical shape has its own characteristics or some properties different from the other figures. Similarly, let us learn some of the properties of a cylinder shape listed below:
- A cylinder has one curved surface and two flat faces which are identical.
- The two circular bases are congruent to each other.
- Its size depends on the radius of the base and the height of the curved surface.
- Unlike a cone, cube, or cuboid, a cylinder does not have any vertex. It means there is no specific corner present in the cylinder.
- The base and the top of the cylinder are identical, i.e it has the same base — either circular or elliptical.
Formulas of Cylinder
Every three-dimensional geometric figure has a minimum of 2 major formulas, surface area, and volume. Likewise, the cylinder has three major formulas related to its surface areas and volume.
- Lateral Surface Area (LSA) or Curved Surface Area (CSA) of cylinder = 2πrh
- Total surface area of cylinder = 2πr(h+r)
- Volume of cylinder = πr2h
In all these formulas, 'r' represents the base radius and 'h' represents the height of the cylinder.
Let us learn about the above cylinder formulas in detail.
Curved Surface Area of Cylinder:
The curved surface area is also termed the lateral surface area. The area formed by the curved surface of the cylinder i.e. space occupied between the two parallel circular bases is known as its CSA. The formula for cylinder curved surface area is given as,
Curved Surface Area (CSA) = 2πrh square units
(Note: ‘h’ is the height, ‘r’ is the radius, and the value of π is 22/7 or 3.14 approximately).
This is because, when the curved face of a cylinder is unfolded, we get a rectangle whose length = circumference of the circle = 2πr and width = height of the cylinder = h. Thus, its area is: length × width = 2πr × h.
Total Surface Area of Cylinder:
The total surface area defines the total area that it occupies including the bases. The cylinder consists of two circles and one curved sheet. So, in order to find out the total surface area of a cylinder, we calculate the curved surface area and the area of two circles.
Curved Surface Area (CSA) = Circumference × Height
CSA= 2πr × h
Area of a Circle = πr2
Total Surface Area (TSA) = Curved Surface Area + 2(Area of a circle)
Total Surface Area (TSA) = 2πrh + 2πr2 = 2πr(h+r) square units
(Note- ‘h’ is the height and ‘r’ is the radius. There are two circles, so we multiply the area of the base circle by 2)
Volume of Cylinder:
The cylinder volume defines the density or amount of space it occupies. If we want a cylinder to fill with water, then the amount of water needed can be calculated by finding its volume.
The volume of a cylinder = Area of a circle × height
Volume = πr2 × h
The volume of a cylinder, V = πr2h cubic units
where ‘h’ is the height and ‘r’ is the radius.
Net of a Cylinder
The net of a cylinder is a 2D structure made by unfolding it. It helps us to visualize the shape of a cylinder and its surface area. When we unfold a cylinder, we get a rectangle joined by two identical circles that form the top and the bottom bases of the cylinder shape. Look at the picture of a cylinder net shown below.
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FAQs on Cylinder Shape
What is a Cylinder?
A cylinder is a 3D shape which consists of two circular bases connected with a curved surface made by folding a rectangle. The top and bottom faces of a cylinder are congruent. It has a total of 3 faces, 2 edges, and no vertices.
What are the Cylinder Formulas?
The three major formulas of the cylinder are:
- Total surface area = 2πr(r+h) square units
- Curved surface area = 2πrh square units
- Volume = πr2h cubic units
What is the Volume of a Cylinder?
The volume of a cylinder is the space occupied by it. It can be calculated using the formula: V = πr2h cubic units.
What is the Surface Area of a Cylinder?
A cylinder has two bases and a curved surface. There are two types of area formulas for a cylinder shape: Curved surface area and Total surface area. The surface area formulas of a cylinder are given below:
- Total surface area = 2πr(r+h) square units
- Curved surface area = 2πrh square units
What are the Real-Life Cylinder Examples?
The real-life examples of a cylinder are: toilet paper rolls, cans, pipes, torches beakers, etc.
How Many Edges Does a Cylinder Have?
A cylinder has 2 edges. An edge is where 2 faces meet. The edge can be straight or can be curved. For example, in a cube, there are 12 straight edges whereas in a cylinder there are 2 curved edges. We know that cylinder is a combination of 2 circles and 1 rectangle. The two straight edges of the rectangle are folded to form the curved edges of the cylinder.
What is a Total Surface Area of Cylinder?
The total surface area of a cylinder is the sum of curved surface area and the area of two circular bases. It is given as:
Total surface area = Curved Surface area + Two circular base areas
Total Surface Area (TSA) = 2πrh + 2πr2 = 2πr(h+r) square units
What is the Base Area of the Cylinder?
The area occupied within the boundary of the circular base of the cylinder is called its base area. The units of the base area of the cylinder are always expressed as square centimeters, square inches, square feet, etc. In geometry, we have a specific formula to find the area of the base of a cylinder that is πr2 where r is the radius of the base.
List All Formulas of Cylinder.
All formulas related to cylinder of radius 'r' and height 'h' are tabulated below:
| Base Area of Cylinder | πr2 |
|---|---|
| Curved Surface Area of Cylinder | 2πrh |
| Total Surface Area of Cylinder | 2πrh+ 2πrr2 |
| Volume of Cylinder | πr2h |
What are the Properties of a Cylinder?
Few properties of a cylinder are listed below:
- It has one curved surface, two curved edges, and two flat circular faces.
- The two flat circular bases are congruent to each other.
- It does not have any vertex.
- The size of a cylinder depends upon the radius of a circular base and its height.
Is Euler's Formula Applicable for Cylinder?
Euler's formula is applicable for 3D shapes that have flat faces only (i.e., it is applicable for Polyhedra). Thus, it is NOT applicable for a cylinder.
How Many Faces Does a Cylinder Have?
There are two flat circular faces and one curved surface present in a cylinder. So, it has a total of 3 faces.