11

A

B

0

22

RELATION BETWEEN THE CENTRAL ANGLE, RELATION BETWEEN THE CENTRAL ANGLE, SECTOR AREA, AND THE LENGHT OF ARCS SECTOR AREA, AND THE LENGHT OF ARCS

BETWEEN TWO SECTORSBETWEEN TWO SECTORS

Look at the picture

33

RELATION BETWEEN THE CENTRAL ANGLE, RELATION BETWEEN THE CENTRAL ANGLE, THE LENGHT OF ARCS, and SECTOR AREATHE LENGHT OF ARCS, and SECTOR AREA

O

C

D

B

A

central AOB

=

The lenght of arc AB

=

The area of sector OAB

central COD

The lenght of arc CD

The area of sector OCD

Look at the picture

44

If central angle is compared to a full If central angle is compared to a full angle of circle that is ( 360angle of circle that is ( 36000), then :), then :

O

B

A

central AOB

=

The lenght of arc AB

=

The area of sector OAB

3600

Circumference of circle

Area of circle

55

If the central angle that be compared to If the central angle that be compared to the full angle of circle ( 360the full angle of circle ( 36000), then :), then :

O

B

A

central AOB =

The lenght of arc AB =

the area of sector OAB

3600 2r r2

66

Example Example 1 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.

77

Solution :Solution :Given :Given :

AB = 40 cm, AOB = 500, AOB = 800

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.

O

D

C

A

B

500

800

Asking :Asking : Find the lenght of arc CD

Answer:Answer:

So, we getSo, we get the lenght of arc CD = 64 cm

88

Example Example 22 : :

O

A

B540

Look at the picture! The lenght of radii = 20 cm, AOB = 540.

Determine the area of sector OAB

99

Given :Given :

AOB = 540, and radii = 20 cm

central AOB =

The area of sector OAB

3600 The area of circle540

=x

3600 r2

X = ( 3 x 1256 ) : 20 = 188,4 cm2.

So, we get the area of sector OAB = 188,4 cm2.

3=

x

20

3,14 x 202

Solution :

1010

1111

Question Question - 1- 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

1212

Given :The lenght of arc PQ = 50 cmThe lenght of arc QR = 75 cm POQ = 450

central POQ=

The lenght of arc PQ

central QOR

The lenght of arc QR45

=50

x 75

X = ( 3 x 45) : 2 = 135 : 2 = 67,50

So, we get QOR = 67,50.

45 = 2

x 3

Solution :

1313

Question Question - 2- 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

CD

B A

600

12 c

m

12 c

m

1414

Given :Radii (1) = 12 cmRadii (2) = 24 cm. AOB = 600

Solution :

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

Asking :the area of the shaded region.

1515

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 cm2 - 75,36 cm2

= 226,08 cm2.

1616

Question - Question - 33

42 cm

Calculate the area of the shaded region as shown in the figure above !

1717

Solution :

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

42 cm

The area of small circle that is shaded =

The area of small circle that isn’t shaded.

1818

1919

Quiz - 1Quiz - 1

Look at the picture, the area of sector OAB =60 cm2,

AOB = 400 and BOC = 120o

Find the area of sector OBC.

O

A

C

1200

400

B

2020

Quiz - 2Quiz - 2

Calculate the area of the shaded region as shown in

the figure above !

14 cm

2121

Given : 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 BOCThe area of sector

OBC400

=60

1200 x

X = 3 x 60 = 180 cm2.

So we get the area of sector OBC = 180 cm2.

1=

60

3 x

Solution Quiz 1 :

2222

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 The area of the shaded region = 154 -

38,5

= 115,5 cm2

14 cm

2323