1. Area Related to circle

2. INTRODUCTION
The concepts of perimeter[circumference] and area of circle Area of two special “parts” of a circular region[or briefly of a circle] known as sector and segment of a circle

3. Perimeter And Area Of A Circle
Perimeter of a circle usually called its circumference circumference = π diameter

4. Circumference = π × diameter = π × 2r [where ‘r’ is the radius of the circle] = 2πr

5. Value of π
According to ARYABHATTA
62832
π =
20000 =

6. According to SRINIVAS RAMANUJAN
The value of π correct to million places of decimals
π is an irrational number and its decimal expansion is non terminating and non-recurring

7. 22
we take the value of π = 7
Area of the circle = πr2

8. Areas of sector and segment of a circle
The portion of a circular region enclosed by two radii and the corresponding arc is called a sector of a circle The portion of the circular region enclosed between a chord and the corresponding arc is called a segment of a circle

9. sector 1-Major sector 2-Angle of sector 3-Minor sector Major sector

10. Segment
Major segment Minor segment

11. The degree measure of angle AOH be Ѳ

12. Unitary method 1- Area of the sector of angle Ѳ
2- length of an arc of a sector of angle Ѳ

13. Area of a sector of angle Ѳ
Circular region to be a sector forming an angle of 3600
When the degree measure of the angle at the center is 3600 ,area of sector = πr2

14. When the degree measure of the angle at the center is 1,area of sector = πr2
360

15. Therefore ,when the degree measures of the angle at the center is Ѳ, area of sector = πr2 × Ѳ
360
= Ѳ × πr2

16. By applying the unitary method and taking the whole length of the circle[or angle3600] as 2πr, we can obtain the required length of the arc APH as Ѳ × 2πr 360

17. Length of an arc of a sector of angle Ѳ

18. Area of segment APH = area of sector OAPH – area of triangle
3600

19. Area of major sector = πr2 – area of minor sector Area of major segment = πr2 – area of minor segment