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    Question

    Length of a minute hand of a clock is 14 cms. Area swept

    bv the minute hand in 5 minutes is:
    A 154 sq cms Correct Answer Incorrect Answer
    B 154/3 sq cms Correct Answer Incorrect Answer
    C 210 sq cms Correct Answer Incorrect Answer
    D 154/√3 sq cms Correct Answer Incorrect Answer

    Solution

    We know that the minute hand completes one rotation in 1 hour or 60 minutes. Therefore, area swept by the minute hand in 60 minutes = Area of the circle with radius equal to the length of the minute hand = πr2 Using unitary method, we get Area swept by minute hand in 1 minute = πr2/60 Thus, area swept by minute hand in 5 minutes = (πr2/60) × 5 = πr2/12 Length of the minute hand (r) = 14 cm It is known that the minute hand completes one rotation in 1 hour or 60 minutes Therefore, the area swept by the minute hand in 60 minutes = πr2 Therefore, the area swept by the minute hand in 5 minutes = 5/60 × πr2 ⇒ 1/12 πr2 = 1/12 × 22/7 × 14 × 14 cm2 = 154/3 cm2

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