1. Length of arc, Area of sector and Perimeter of sector

2. Length of arc A B
Arc AB r
Consider a circle of radius r. The length of the circle is the same as circumference of the circle which is equal to 2πr. The red part is called an arc. The name of the arc is The length of the arc is a part of the circumference of the circle. AB

3. Central angle of sector
The length of an arc is equal to ratio of central angle(Ɵ) of the sector to central angle of the circle(3600) multiplied by the circumference of the circle.
Central angle of sector
Central angle of circle
Length of the arc =
x Circumference of circle Ɵ
∴ Length of the arc =
For a full circle, the central angle of the sector is equal to central angle of
circle(Ɵ) which is 360o. So, the length of the full circle is
2πr
which is the circumference of the circle.

4. Example 1: Find the length of arc of quadrant of a circle with radius 21 cm.
Solution:
Given: Radius (r) = 21 cm To Find: Length of the quadrant
We know that if a circle is divided into 4 equal sectors we will get 4 quadrants.
Therefore, the central angle(Ɵ) of a quadrant =
Length of the arc =
Length of the quadrant =
Length of the quadrant =
= x 3 = 33 cm
Ans: Length of the quadrant = 33 cm 1 4 11 3
(substituting π = and r = 21) 2

5. Example 2: Find the length of arc of semicircle of a circle with radius 14 cm.
Solution:
Given: Radius (r) = 14 cm To Find: Length of the semicircle
We know that if a circle is divided into 2 equal sectors we will get 2 semicircles.
Therefore, the central angle(Ɵ) of a quadrant =
Length of the arc =
Length of the semicircle =
Length of the semicircle =
= x 2 = 44 cm
Ans: Length of the semicircle = 44 cm
(Dividing 180 and 360 by 2) 2 2
(substituting π = and r = 14)

6. Try These
The radius of a sector is 21cm and its central angle is 120 ° . Find
the length of the arc
area of the sector and
perimeter of sector