In Perimeter of circle lesson, we are going to discuss,

What is the Perimeter of circle or circumference of circle

Circumference equation or circumference formula
 Perimeter of semicircle
 Perimeter of quarter circle
 Perimeter of sector
What is the Perimeter of Circle
Before moving into perimeter let’s recall some knowledge about key features of circle.
 Center of Circle
 Diameter of Circle
 Radius of Circle
Center of Circle
The center is the exact midpoint of the circle.
In other words, we can also define the Center as the point at which the axis of symmetry of a circle intersects is the center.
Diameter of Circle
Diameter is a straight segment joining two points on a circle, which passes through the center of the circle.
In this circle, A B is the diameter.
Radius of Circle
The straight line segment joining the center to any point on the circle is called a Radius of a circle.
If the center is ‘O’ and the point on the circle is ‘B’ then, OB is the radius of the circle.
OB and OD are ‘Radii’ (plural form of the radius.) of the circle.
There is a relationship between diameter and radius
Diameter – AB
Radii – AO and BO
AB = AO + BO
AB = AO + AO ; because BO = AO
AB = 2 AO
Diameter = 2 x radius
The diameter of a circle is twice it’s radius.
The simple meaning of perimeter is length around a closed plane figure
When it comes to circles we also called it the circumference of circle
Circumference Formula
For full circle
If ‘O’ is the center and ‘r’ is the radius of this circle.
The circumference ‘c’ will be,
c = 2πr
Here π is a constant value.
Example 01:
Find the circumference of a circle of radius 14cm.
Circumference c = 2πr
Therefore the circumference is 88cm.
When the diameter is given instead of the radius we have another circumference equation.
Let ‘d’ be the diameter and ‘r’ is the radius.
d = 2πr (two times radius equal to diameter)
If the circumference of the circle denoted by ‘c’
c = 2πr
We can also write circumference of a circle formula as,
c = 2πr
c = π x d (d = 2πr)
c = πd
Example 02:
Find the circumference of a circle of diameter 21cm.
This example is about the diameter to circumference.
Therefore the circumference is 66cm.
Exercise 01
Find the circumference of the circle with the measurements given below.
 Radius 7cm
 Diameter 28m (hint: convert into mixed number)
 Diameter 1712cm
 Radius 10.5m
*Answers are given at the end of this article.
Perimeter of Semicircle
When a circular lamina separated into two equal parts along a diameter each part is known as a semicircle.
The arc length of the semicircle of radius
It is clear from the figure that, to find the perimeter of a semicircle, the diameter should be added to the arc length.
The perimeter of a semicircle of radius
Example 03:
Find the perimeter of semicircle when the diameter is 21cm.
You can refer multiplication of fractions article to learn simplifications.
2r = diameter = 21cm
Therefore the perimeter of the semicircle
= 33cm + 21cm
= 54cm
Exercise 02:
Find the perimeter of the semicircular lamina with the measurements given below.
 Radius = 14cm
 Diameter = 7cm
*Answers are given at the end of this article.
Perimeter of Quarter Circle
The arc length of the quarter circle
It is clear from the figure that, to find the perimeter of a quarter circle, two radii should add to the arc length.
The perimeter of quarter circle
Example 04:
If the radius is 28cm, find the perimeter of the quarter circle.
Therefore the perimeter of the quarter circle
= 44cm + 56cm
= 100cm
Perimeter of a Circle Sector
A region bounded by two radii and an arc is called a sector of a circle.
The angle subtended at the center of the circle by the arc is called the central angle.
Here the central angle is ‘θ‘
The angle at the center of the circle is 360^{o}. The arc length related to the 360^{o} angle is 2πr.
By looking at the above diagram we can say that,
For 360^{o} the arc length will be 2πr.
The arc length of a sector of a circle with radius ‘r’ and central angle ‘π‘.
Example 05:
Find the perimeter
Arc length is 11cm.
Therefore the perimeter of the sector
= 11cm + 2 x 9cm
= 11cm + 18cm
= 29cm
Answers
Exercise 01
Exercise 02
Calculator for Semi Circles  Area and Perimeter
Radius, diameter, Perimeter and area calculation option are available. Select what you need to find and enter the number in text box. Then click ‘submit’.
Always remember this calculator is only checking for your answers. You have to do the exercises your self.