Cylinder is a three-dimensional solid figure, in geometry, which has two parallel circular bases joined by a curved surface, at a particular distance from the center. Toilet paper rolls, plastic cold drink cans are real-life examples of cylinders. The cylinder has two major properties, i.e., surface area and volume. In the late 14th century, the word "cylinder" is derived from Latin (Cylindrus) and Greek (Kylindros) words, which mean "roll", "roller", and "tumblr". In this chapter, we are going to look at the cylinder formula, cylinder volume, cylinder surface area. Also, do you know? The Leaning Tower of Pisa is cylindrical in shape. Let us read more about a cylinder.
|1.||Definition of Cylinder|
|2.||Types of Cylinder|
|3.||Properties of Cylinder|
|4.||Formulas of Cylinder|
|5.||FAQs on Cylinder|
Definition of Cylinder
A cylinder is a three-dimensional solid shape that consists of two parallel bases linked by a curved surface. These bases are like a circular disk in a shape. The line passing from the center or joining the centers of two circular bases is called the axis of the cylinder. The distance between the two bases of the cylinder 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 as is represented by “r”. The cylinder is a combination of 2 circles + 1 rectangle. Look at the given image showing the formation of the cylinder.
Types of Cylinder
We just read about some real-life examples of a cylinder, which shows cylinders can be of various types. In geometry, there are four different types of cylinders. They are:
- Right circular cylinder: If the axis of the two parallel lines is perpendicular to the center of the base, it is called the right circular cylinder.
- Oblique cylinder: An oblique cylinder is one whose sides lean over the base. In an oblique cylinder, the sides are not perpendicular to the center of the base. The Leaning Tower of Pisa is a real-world example of an oblique cylinder.
- Elliptic cylinder: A cylinder whose base is in the form of an ellipse is called an elliptic cylinder.
- A right circular hollow cylinder or cylindrical shell: The right circular hollow cylinder also called a "cylindrical shell", 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.
Properties of Cylinder
Every geometrical shape has its own characteristics or some properties different from the other figures. Similarly, there are a few properties that define a cylinder.
- By cylinder definition, it has two curved edges, one curved surface, and two flat faces.
- The two circular bases are congruent to each other.
- The size of the cylinder depends on the radius of the base and the height of the curved sheet.
- Cylinder is termed to be a “Right Cylinder”, if the axis forms a right angle with the bases, exactly over each other.
- Cylinder is termed to be an “Oblique Cylinder”, the axis does not form a right angle with the bases, and is not over each other.
- 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 they have the same base — either circular or elliptical.
Formulas of Cylinder
Every three-dimensional geometric figure has 2 major formulas, area, and volume. Likewise, the cylinder has three major formulas related to area and volume.
- Lateral Surface Area or curved surface area
- Total Surface Area
Let us learn about the mentioned formulas in detail.
- Curved Surface Area of Cylinder: The curved surface area is also termed a 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 CSA. The formula for CSA is given as Curved Surface Area (CSA) = 2πrh square units
(Note- ‘h’ is the height and ‘r’ is the radius.)
- Total Surface Area of Cylinder: The total surface area of a cylinder defines the total area that it occupies. 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 by 2)
- Volume of Cylinder: The cylinder volume defines the density or amount of space it occupies.
The volume of a cylinder = Area of a circle × height
Volume = 𝛑r2 × h
The volume of a Cylinder, V = πr2h cubic units
(Note- ‘h’ is the height and ‘r’ is the radius.)
☛ Related Articles on Cylinder
Check out the following pages related to the cylinder.
Example 1. Britt wants to buy a can that can hold 1 gallon of oil. The radius of the can is 5 inches. Help Britt find the height of the can she has to buy. Hint: The can is in the form of a cylinder.
Volume V= 1 gallon
1 gallon= 231 cubic inches
Radius r = 5 inches
The volume of a cylinder V = 𝛑r2h
231 = 22/7 × (5)2 × h
(231 × 7)/(22 × 25) = h
h = 2.94 inches.
Therefore, the height of the can should be 2.94 inches.
Example 2. Emma has an old cylindrical water tank at her home. The radius is 40 inches and the height is 150 inches. She wants to replace it with a new one with the same dimensions. Help Emma figure out the area of the water tank.
The water tank is in the form of a cylinder.
Total Surface Area of a cylinder = 2𝛑r(h+r)
TSA = 2 × 22/7 × 40(150 + 40)
TSA = 2 × 22/7 × 7600
TSA = 47,771.42 sq.inches
Area of the water tank = 47,771.42 sq.inches.
Example 3. What is the volume of the cylinder with a radius of 5 units and a height of 8 units?
Radius,r = 5 units
Height,h = 8 units
Volume of the cylinder, V = πr2h cubic units.
V = (22/7) × 52 × 8
V = 22/7 × 25 × 8
V= 628.57 Cubic units.
Therefore the volume of the cylinder is 628.57 cubic units.
FAQs on Cylinder
What is a Cylinder in Geometry?
A cylinder is a three-dimensional solid figure which consists of two circular bases connected with two parallel lines. These two parallel lines form a curved surface which is bounded by two circles at the top and the bottom.
What are the Real-Life Cylinder Examples?
The real-life examples of a cylinder are: toilet paper rolls, cans, pipes, torches.
What are the Two Major Formulas of Cylinder?
The two major formulas of the cylinder are:
- Total surface area = 2πr(r+h) square units
- Volume of cylinder = πr2h cubic units
How Many Edges Does a Cylinder Have?
A cylinder has 2 edges. An edge is where 2 faces meet. 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?
Total surface area of a cylinder is a sum of cum of curved surface area and area of two circular bases. It is given as:
Total surface area = Curved Surface area + Two circular base areas
Total Surface Area (TSA) = 2𝛑rh + 𝛑r2 = 2𝛑r(h+r) square units.
What is the Base Area of Cylinder?
The area occupied within the boundary of the circular base of the cylinder is called the base area of the cylinder. 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 of the cylinder.
What do you Mean by the Area of a Cylinder Calculator?
The area of a cylinder calculator is an online tool that helps to calculate the area of a cylinder for a given radius and height within a few seconds. Try now Cuemath's Area of a Cylinder Calculator for fast calculations.
- Volume of Cylinder Calculator
- Height of a Cylinder Calculator
- Radius of a Cylinder Calculator
- Volume of a Cylinder Calculator
Describe the Properties of Cylinder.
Few properties of cylinder are listed below:
- Cylinder has one curved surface, two curved edges, and two flat circular faces.
- The two flat circular bases are congruent to each other.
- A cylinder does not have any vertex
- The base and the top of the cylinder are identical.
- The size of a cylinder depends upon the radius of a circular base and its height.
How Many Sides Does a Cylinder Have?
There are two flat circular faces and one curved surface area present in a cylinder. In a cylinder, we do not use the word "sides" since the cylinder has a curved surface