1. CIRCLE

2. RELATION BETWEEN THE CENTRAL ANGLE, SECTOR AREA, AND THE LENGHT OF ARCS BETWEEN TWO SECTORS
Look at the picture

3. RELATION BETWEEN THE CENTRAL ANGLE, THE LENGHT OF ARCS, and SECTOR AREA 
Look at the picture
central  AOB =
The lenght of
arc AB
The area of sector OAB
central  COD
arc CD
The area of sector OCD

4. Circumference of circle
If central angle is compared to a full angle of circle that is ( 3600), then : O B A 
central  AOB =
The lenght of arc AB
The area of sector OAB
3600
Circumference of circle
Area of circle

5. If the central angle that be compared to the full angle of circle ( 3600), then :
central  AOB =
The lenght of arc AB
the area of sector OAB
3600
2r
r2

6. Example 1 : O D C A B
500
800
Look at the picture beside, the lenght of arc AB = 40 cm, AOB = 500, and AOB = 800.
Find the lenght of arc CD.

7. Solution : Given : AB = 40 cm, AOB = 500, AOB = 800D C A B
500
800
Asking : Find the lenght of arc CD
Answer:
central  AOB =
The lenght of arc AB
central  COD
The lenght of arc CD
500 =
40 cm
800
X cm
X = ( 40 x 80 ) : 50 = 64.
So, we get the lenght of arc CD = 64 cm

8. Example 2 :
Look at the picture! The lenght of radii = 20 cm, AOB = 540.
Determine the area of sector OAB O A B
540

9. Solution : Given : AOB = 540, and radii = 20 cm 540 = x 3600 r2 3 =
central  AOB =
The area of sector OAB
3600
The area of circle
540 = x
3600
r2 3 = x 20
3,14 x 202
X = ( 3 x 1256 ) : = 188,4 cm2.
So, we get the area of sector OAB = 188,4 cm2.

10. EXERCISE

11. Question - 1
Look at the picture, the lenght of arc PQ = 50 cm, the lenght of arc QR = 75 cm and POQ = 450. Determine QOR. O P R
450 Q

12. Solution : 45 = 50 x 75 45 = 2 x 3 X = ( 3 x 45) : 2 = 135 : 2 = 67,50
Given :
The lenght of arc PQ = 50 cm
The lenght of arc QR = 75 cm
POQ = 450
central  POQ =
The lenght of arc PQ
central  QOR
The lenght of arc QR 45 = 50 x 75 45 = 2 x 3
X = ( 3 x 45) : 2 = 135 : 2 = 67,50
So, we get  QOR = 67,50.

13. Question - 2 Look at the picture, COD = 600, the lenght of
OA = 12 cm and AC = 12 cm.
Calculate the area of the shaded region. O C D B A
600
12 cm

14. Area of sector OAB = 60/360 x area of circle = 1/6 x 3,14 x 12 x 12
Solution :
Given :
Radii (1) = 12 cm
Radii (2) = 24 cm.
AOB = 600
Asking :
the area of the shaded region.
Answer:
Area of sector OAB = 60/360 x area of circle
= 1/6 x 3,14 x 12 x 12
= 3,14 x 24
= 75,36 cm2

15. Area of sector OCD = 60/360 x area of circle
= 1/6 x 3,14 x 24 x 24
= 3,14 x 96
= 301,44 cm2
The area of the shaded region:
= area of sector OCD - area of sector OAB
= 301,44 cm ,36 cm2
= 226,08 cm2.

16. Question - 3
42 cm
Calculate the area of the shaded region as shown in the figure above !

17. Solution : The area of circle that is shaded : L = ½  r2
42 cm
The area of circle that is shaded :
L = ½  r2
= ½ x 22/7 x 21 x 21
= ½ x 22 x 63
= 11 x 63
= 693 cm2
The area of small circle that is shaded =
The area of small circle that isn’t shaded.

18. QUIZ

19. Quiz - 1 Look at the picture, the area of sector OAB =60 cm2,
1200
400 B
Look at the picture, the area of sector OAB =60 cm2,
AOB = 400 and BOC = 120o
Find the area of sector OBC.

20. Calculate the area of the shaded region as shown in the figure above !
Quiz - 2
14 cm
Calculate the area of the shaded region as shown in the figure above !

21. Solution Quiz 1 : 400 = 60 1200 x 1 = 60 3 x X = 3 x 60 = 180 cm2.
Given : AOB = 400 and BOC = 1200
The area of sector OAB = 60 cm2
Asking: The area of sector OBC.
Answer:
central  AOB =
The area of sector OAB
central  BOC
The area of sector OBC
400 = 60
1200 x 1 = 60 3 x
X = 3 x 60 = cm2.
So we get the area of sector OBC = 180 cm2.

22. Solution Quiz 2 : The area of circle that is shaded : Lb =  r2
= 22/7 x 7 x 7
= 154 cm2
Lk =  r2
= 22/7 x 3,5 x 3,5
= 38,5 cm2
14 cm
The area of the shaded region = ,5
= 115,5 cm2

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