Question

 

A chord of a circle of
radius 15cm subtends an angle of 60° at the center. Find the areas of the
corresponding minor and major segments of the circle.

 

Answer 1

the procedure is -fist find the area of minor sector.
the formula is( Θ/360)πr^2.
Then find the area of the triangle and subtract it frm the sector's area.
and then you will get minor segment's area .
now,for the major segmeny's area ,calculate the area of the cirlcle ,and subtract the area of the minor segment from it.

Answer 2

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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