Math, asked by RAJIB171, 1 year ago

A chord of a circle, of radius 15 cm, subtends an angle of 60 at the centre of the circle. Find the area of major and minor segments (take = 3.14, 3 = 1.73)

Answers

Answered by akhilvinayak03
21

Answer: (Rounded off values)

Minor - 20.47 cm² and Major - 686.03 cm²

Step-by-step explanation: given below

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Answered by ananya88874
23

Answer:

In the mentioned figure,

O is the centre of circle,

AB is a chord

AXB is a major arc,

OA=OB= radius = 15 cm

Arc AXB subtends an angle 60 °

at O.

Area of sector AOB=

=60/360 ×π×r ²

= 60/360 ×3.14×(15) ²

=117.75cm ²

Area of minor segment (Area of Shaded region) = Area of sector AOB− Area of △ AOB

By trigonometry,

AC=15sin30

OC=15cos30

And, AB=2AC

∴ AB=2×15sin30=15 cm

∴ OC=15cos30=15'2

=15× 2

1.73

=12.975 cm

∴ Area of △AOB=0.5×15×12.975=97.3125cm ²

∴ Area of minor segment (Area of Shaded region) =117.75−97.3125=20.4375 cm ²

Area of major segment = Area of circle − Area of minor segment

=(3.14×15×15)−20.4375

=686.0625cm²

@ananya

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