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B

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RELATION BETWEEN THE CENTRAL ANGLE,

SECTOR AREA, AND THE LENGHT OF ARCSBETWEEN TWO SECTORS

Look at the

picture

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

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

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If central angle is compared to a full angle of circle

that is ( 3600), then :

O

central AOB=

The lenght of

arc AB=

The area of

sector OAB

3600

Circumference

of circle Area of circle

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If the central angle that be compared to the full

angle of circle ( 3600), then :

O

central AOB =

The lenght of

arc AB =

the area of

sector OAB

3600 2r r2

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Example 1 :

O

D

C

A

B

50

0

800

Look at the picture beside,

the lenght of arc AB = 40

cm, AOB = 500, and

AOB=800.

Find the lenght of arc CD.

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Solution :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 : Find the lenght of arc CD

Answer:

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

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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 :

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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

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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 QR

45=

50

x 75

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

So, we get QOR = 67,50.

45=

2

x 3

Solution :

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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.

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Given :

Radii (1) = 12 cm

Radii (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 shadedregion.

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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

2

- 75,36 cm

2

= 226,08 cm2.

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Question - 3

42 cm

Calculate the area of the shaded

region as shown in the figure above !

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Solution:

The area of circle that

is shaded :

L = r2

= x 22/7 x 21 x 21

= 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 isnt shaded.

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Quiz - 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

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Quiz - 2

Calculate the area of the shaded

region as shown in the figure above !

14 cm

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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

X = 3 x 60 = 180 cm2.

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

1=

60

3 x

Solution Quiz 1 :

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Solution Quiz 2:

The area of circle thatis 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

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