In the adjoining figure O is the centre of a circle if OA = 10 cm, OB = 15 cm and angle BOD = 720 then the area of shaded region is( cm2) (A) 5 (B) 10 (C) 25π (D) 35π8
Answers
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Given :- In the adjoining figure O is the centre of a circle if OA = 10 cm, OB = 15 cm and angle BOD = 72°
To Find :- Area of shaded region ?
Solution :-
We know that,
- Area of sector = (Angle at centre/360°)πr²
So,
→ Radius of sector OAC = 10 cm
→ Angle at centre = 72°
then,
→ Area of sector OAC = (72°/360°) * π * (10)²
→ Area of sector OAC = (1/5) * π * 100
→ Area of sector OAC = 20π cm²
similarly,
→ Radius of sector OBD = 15 cm
→ Angle at centre = 72°
then,
→ Area of sector OBD = (72°/360°) * π * (15)²
→ Area of sector OBD = (1/5) * π * 225
→ Area of sector OBD = 45π cm²
therefore,
→ Shaded Area = Area of sector OBD - Area of sector OAC
→ Shaded Area = 45π - 20π
→ Shaded Area = 25π cm² (C) (Ans.)
Hence, area of shaded region is equal to 25π cm² .
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