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Class 10>>Maths>>Areas Related to Circles>>Area of Sector and Length of an Arc>>A chord of a circle of radius 10 cm subt

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)

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Solution

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In the mentioned circle,

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

AB is a chord which subtents 90o at centre O, i.e., ∠AOB=90o

(i)

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

=(4π×10×10)−(0.5×10×10)

=78.5−50

=28.5cm2

(ii)

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

= (π×10×10)−(4π×10×10)

=314−78.5

=235.5cm2

Verified answer

In the mentioned circle,

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

AB is a chord which subtents 90o at centre O, i.e., ∠AOB=90o

(i)

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

=(4π×10×10)−(0.5×10×10)

=78.5−50

=28.5cm2

(ii)

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

= (π×10×10)−(4π×10×10)

=314−78.5

=235.5cm2

.