A part of a circle that is formed by an arc and two radii of a circle is said to be the sector of a circle. From the below figure the colored area is called a sector. The sector can be assumed as a slice of a pizza.(images will be updated soon).
A sector is represented by sector OAB where angle ABC is θ and r represents the radius of the circle.
A circle is divided into two sectors, namely the major sector, and the minor sector.
A larger part of the circle occupied by the radii and the major arc is said to be a major sector.
In the figure the yellow colored part is the major sector.(image will be updated soon)
A smaller part occupied by two radii and a minor arc is called the minor sector.
In the figure, the blue-colored part is a minor sector.(image will be updated soon)
Consider a circle with O as center and r as the radii of the circle. Let OAB is the minor sector such that angle AOB = θ . θ is less than 1800.
Now if increases, the length of the arc AB also increases if = 1800 then arc AB becomes the circumference of a semi-circle that is πr.
Therefore, Arc length l = θ/180 x πr
If the arc is subtended for the whole circle the length of the arc
Can also be written as, l = θ/360 x circumference of a circle
If the arc subtends an angle , then the area of the corresponding sector is
Can also be written as, A =θ/360 x area of the circle
The perimeter of a circle sector is the sum of the two radii and the subtended arc length of a circle. Perimeter of a circle sector is also called the circumference of a sector.(image will be updated soon)
Consider the above figure, here the yellow colored part is the minor sector.
The perimeter of sector of circle formula is given below :
Perimeter of sector/circumference of a sector = 2 x radius + arc length
Arc length is also calculated as
Arc length = θ/360 x 2πr
Arc length = r x (2θπ/360 )
Arc length = radius × central angle
Therefore, the perimeter of a sector formula is also given as:
Let us understand how to calculate the perimeter of a sector or circumference of a sector by the solved example.
Example 1: Find the area of a sector of a circle whose radius is 28cm and the central angle is 450.
Solution: We know that the area A of a sector of a circle is given by
A = θ/360 x πr2
Here, r = 28 cm and θ= 450
A = 45/360 x 22/7 x 28 x 28
A = 308 cm2
Example 2: The perimeter of a sector of a circle of radius is 5.2cm is 16.4 cm. Find the area of the sector.
Solution: Perimeter of sector of circle formula is given by
Perimeter of sector = 2 radius + arc length
Here, r = 5.2 cm and perimeter of sector = 16.4 cm
16.4 = 2 x 5.2 + arc length
Arc length = 16.4 - 10.4
Arc length = 6cm
Also we have,
Area of sector = ½ lr
= ½ x 6 x 5.2
1.What is the Circumference of the Circle and how It is Calculated?
Answer : The distance around the circle or you can say the boundary of the circle is said to be circumference of a circle. Circumference can also be said as the length of a circle.(image will be updated soon)
The circumference of a circle is calculated by just multiplying pi with the diameter of the circle. Pi is represented as and it has the constant value of 22/7 or 3.141592653589793 or simply 3.14.
π is defined as the ratio of circumference of a circle with the diameter. For any circle the value of π is almost the same.
Therefore to find the circumference of a circle we have the formula
Circumference of a circle = πd, where d is the diameter of the circle.
It can be written in the form of radius as
Circumference of a circle = π 2r = 2πr.
2. What is the Segment of a Circle?
Answer: When a chord of a circle divides the circle into two regions, then the region enclosed by an arc and a chord is said to be a segment of the circle. A chord divides the circle into two segments, major segment, and minor segment.
If the boundary of a segment is a minor arc of a circle, then the corresponding segment is called a minor segment.
A segment corresponding to the major arc of a circle is known as a major segment.
In the figure below ACB is a minor segment and ADB is a major segment.(image will be updated soon).