a chord of a circle of radius 5 cm subtends an angle of 45 degree at the centre find the area of minor segment of the circle
Answers
Answer:
686.0625
Step-by-step explanation:
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
o
at O.
Area of sector AOB=
360
60
×π×r
2
=
360
60
×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
3
=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
=686.0625cm
2
Answer:your answer is 9 cm² approx
Don't beleive you should calc
Step-by-step explanation: