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    Question

    A circle has a radius of 15 cm, and a chord subtends a central angle of 60° at the center. Find the area of the segment formed by the chord.

    A 20.325 cm² Correct Answer Incorrect Answer
    B 30.50 cm² Correct Answer Incorrect Answer
    C 24.725 cm² Correct Answer Incorrect Answer
    D 40.75 cm² Correct Answer Incorrect Answer

    Solution

    Area of sector = (θ/360) × πr² = (60/360) × π(15)² = (1/6) × π(225) = 117.75 cm². Area of triangle = (1/2) × base × height = (1/2) × 15 × (15 × √3 / 2) = 97.425 cm². Area of segment = 117.75 – 97.425 = 20.325 cm².

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