Question

a chord of a circle of diameter 12 cm makes an angle of 30° at the center. Find the area of the minor segment ​

Answer 1

Answer:

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>>A chord of a circle of radius 30 cm mak

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A chord of a circle of radius 30 cm makes an angle of 60

∘

at the centre of the circle. Find the areas of the minor and major segments. [take π=3.14 and

3

=1.73 ].

Medium

Solution

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Radius of circle =r=30 cm

Area of minor segment = Area of sector – Area of triangle … (1)

Area of major segment = Area of circle – Area of minor segment …(2)

Area of sector =

360

θ

×πr

2

=

360

60

×3.14×30×30=471 cm

2

Area of triangle =

4

3

(side)

2

(Since it forms an equilateral triangle)

=

4

3

×30×30=389.7 cm

2

Area of minor segment =471–389.7=81.3 cm

2

[using (1)]

Area of major segment =π(30

2

)−81.3=2744.7 cm

2

[using (2)]