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Cylinder | Shape, Formula and Examples

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A cylinder is a three-dimensional geometric shape with two circular bases connected by a curved surface. It has a total of 3 faces, 2 edges, and no vertices.

Illustration of a Cylinder

Let’s learn the definition, properties, and formulas related to Surface Area, and Volume of Cylinder in detail.

Cylinder Definition

A cylinder is defined as a solid shape with two circular bases connected by a lateral surface known as the curved surface.

  • The distance between the two parallel circular bases of the cylinder is referred to as the height (h) of the cylinder.
  • The line connecting the centres of the two circular bases is the axis of the cylinder.
  • The radius (r) of cylinder is the distance from the centre to the outer boundary of a cylinder. 

Cylinder Shape

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

In a right cylinder, the centers of these circular bases align directly above each other. The straight line connecting these centers is called the axis and represents the cylinder’s height.

When viewed from above, the cylinder appears as a circle, while from the side, it resembles a rectangle.

Cylinder Faces Vertices Edges

Any 3-D figure has faces, vertices, and edges which define the features of that figure. The two circular faces of the cylinder are parallel to each other and the distance between them is the height of the cylinder.

  • Faces: In a cylinder, there are a total of 3 faces i.e. 2 flat circular faces + 1 curved face
  • Edges: In a cylinder, there are 2 circular edges one at the top face and one at the bottom face.
  • Vertices: In a cylinder, there are 0 vertices.

Cylinder Properties

Key properties of the cylinder are:

  • Bases of cylinders are always congruent and parallel to each other.
  • A cylinder has two flat faces which are identical to each other and one curved surface.
  • Volume and Area of any cylinder are proportional to the radius and height of the cylinder.

Types Of Cylinder

Cylinders are classified into various types, such as: right circular cylinders, Oblique Cylinders, Elliptical Cylinders, and Cylindrical shells or Hollow Cylinders. 

Types Of Cylinder

Illustration of Different Types of Cylinders

Type of Cylinder Description
Right Circular Cylinder A cylinder where the axis is perpendicular to the center of the base.
Oblique Cylinder A cylinder where the axis is not perpendicular to the center of the base, meaning the axis forms an angle other than a right angle with the center of the base.
Elliptical Cylinder A cylinder with elliptical-shaped bases.
Cylindrical Shells or Hollow Cylinders These are made of two right-circular cylinders, one inside the other, creating a hollow space. The axis is perpendicular to the central base and is common to both cylinders. Examples include hollow pipes and toilet paper rolls.

Cylinder Formulas

A cylinder has two major formulae, i.e., surface area and volume. A cylinder has two kinds of surface areas: the curved surface area or the lateral surface area, and the total surface area.

So, the three major formulae related to a cylinder are :

Property Formula
Volume (V) V = πr²h
Curved Surface Area (CSA) CSA = 2Ï€rh
Total Surface Area (TSA) TSA = 2πrh + 2πr² = 2πr(h + r)

Basic Dimensions of Cylinder

Volume of Cylinder

The volume of a cylinder is the density or amount of space occupied by the cylinder.

Let us assume that a cylindrical-shaped container is filled with refined oil. Now, to calculate the amount of oil, we need to determine the volume of the cylindrical-shaped container.

Now, the volume of a cylinder = Area of a circle × height

Volume (V) = πr2 × h cubic units

Volume of Cylinder Formula :

Volume of a cylinder =  (πr2h) cubic units

Where, 

  • r is the radius of the cylinder, and 
  • h is the height of the cylinder.

Read More On :

Curved Surface Area (CSA) of Cylinder

The curved surface area, or lateral surface area of a cylinder, is the space enclosed between the two parallel circular bases.

The formula for the curved surface area, or lateral surface area, of a cylinder, is given as,

Curved Surface Area (CSA) = Circumference × Height

Formula of CSA of cylinder :

Curved Surface Area (CSA) = 2Ï€rh

where, 

  • r is the radius of the cylinder, and 
  • h is the height of the cylinder.

Read More On:

Total Surface Area (TSA) of Cylinder

The total surface area of a cylinder is the sum of the area of the curved surface or lateral surface and the areas of the two circular bases.

We know that, 

Curved Surface Area (CSA) = (2 π r h) square units

Area of a Circle = πr2 square units

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

Formula for the TSA of a cylinder :

Total Surface Area (TSA) = [2Ï€r(h + r)] square units

where, 

  • r is the radius of the cylinder, and 
  • h is the height of the cylinder.

Related :

Solved Examples on Cylinder

Let’s solve some example problems using the formulas related to cylinder.

Example 1: Determine the curved surface area of the cylinder with a radius of 8 inches and a height of 15 inches.

Solution:

Given,

Radius = 7 inches and

The height of the cylinder = 15 inches.

We have,

The curved surface area of the cylinder = (2Ï€rh) square units

⇒ CSA of Cylinder = 2 × (22/7) × 8 × 15

⇒ CSA of Cylinder = 754.285 sq. in

Hence, the curved surface area of the cylinder is 754.285 sq. in.

Example 2: Calculate the volume of a cylindrical-shaped water container that has a height of 18 cm and a diameter of 12 cm.

Solution:

Given: Height = 18 cm, 

Diameter = 12 cm

As Diameter = 2 × radius,

⇒ 2 × radius = 12 cm

⇒ r = 6 cm

We have,

Volume of Cylinder =  (π r2 h) cubic units

⇒ V = (22/7) × (6)2 × 18

⇒ V = 2,034.72‬ cm3

Hence, volume of the cylindrical-shaped water container is 2034.72 cm3.

Example 3: Determine the height of the cylinder if its volume is 625 cubic units and its radius is 5 units.

Solution:

Given: Volume = 625 cubic units, and 

Radius = 5 units

Let the height of the cylinder be h units.

We know that, Volume of a cylinder =  π r2 h

⇒ 625 = (22/7) × (5)2 × h

⇒ h = (625/25) × (7/22)

⇒ h = 7.95 units

Hence, height of the given cylinder is 7.95 units

Example 4: Find the radius of the cylinder if its curved surface area is 550 sq. cm and its height is 14 cm.

Solution:

Given: Curved Surface Area of cylinder = 550 sq. cm, and 

Height of Cylinder = 14 cm

Let the radius of cylinder be r cm.

We know that, Curved Surface Area of the cylinder = 2Ï€rh

⇒ 550 = 2 × (22/7) × r × 14

⇒ 88r = 550 

⇒ r = 550/88

⇒  r = 6.25 cm

Hence, radius of ‬the given cylinder is 6.25 cm.

Cylinder- FAQs

1. What is a Cylinder?

A cylinder is defined as a three-dimensional geometric shape with two parallel and congruent circular bases connected by a curved surface.

2. What is Volume of Cylinder Formula?

The formula of volume of Cylinder is as follows :

V = πr²h units3

3. How To Find CSA of Cylinder ?

We use the following formula to find CSA of Cylinder :

Curved Surface Area = 2Ï€rh units2

4. How To Find TSA of Cylinder ?

The TSA of Cylinder is calculated using the following formula:

Total Surface Area = 2Ï€r(r+h) units2

5. How many vertices and edges does a cylinder have?

A cylinder has zero vertices and two edges.

6. How many bases does a cylinder have?

A cylinder has two circular bases one at the bottom and one at the top.



Last Updated : 18 Feb, 2024
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