Question
In a circle of radius 7 cm, the area of a sector is
(154/3) cm². Find the angle of the sector at the centre.Solution
Area of a sector = (θ/360) × πr² Given: (θ/360) × π × 7² = 154/3 π ≈ 22/7, but notice: πr² = π × 49. They gave 154/3; check with π=22/7: πr² = (22/7)×49 = 22×7 = 154 So (θ/360) × 154 = 154/3 Cancel 154 (non-zero): θ/360 = 1/3 ⇒ θ = 120°.
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