6. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas
of the corresponding minor and major segments of the circle.
(Use Te = 3.14 and 13 = 1.73)
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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
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