Question

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:

⇒(i) minor segment

⇒(ii) major sector. (Use π = 3.14)

Answer 1

Answer:

In the mentioned circle,

O is the centre and AO =BO = Radius = 10 cm

AB is a chord which subtents 90

o

at centre O, i.e., ∠AOB=90

o

(i)

Area of minor segment APB (Shaded region) = Area of Sector AOB - Area of △AOB

=(

4

π×10×10

)−(0.5×10×10)

=78.5−50

=28.5cm

2

(ii)

Area of Major sector = Area of circle - Area of Sector AOB

= (π×10×10)−(

4

π×10×10

)

=314−78.5

=235.5cm

2

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Answer 2

Answer:

Step-by-step explanation:

In the mentioned circle,

O is the centre and AO =BO = Radius = 10 cm

AB is a chord which subtents 90

o

at centre O, i.e., ∠AOB=90

o

(i)

Area of minor segment APB (Shaded region) = Area of Sector AOB - Area of △AOB

=(

4

π×10×10

​

)−(0.5×10×10)

=78.5−50

=28.5cm

2

(ii)

Area of Major sector = Area of circle - Area of Sector AOB

= (π×10×10)−(

4

π×10×10

​

)

=314−78.5

=235.5cm