10th Class Mathematics Areas Related to Circles Question Bank Case Based (MCQs) - Areas Related to Circles

  • question_answer
    Study Case : Q. 26 to 30
    Kritika bought a pendulum clock for her living room. The clock contains a small pendulum of length\[\text{15cm}\]
    The minute hand and hour hand of the clock are \[\text{9 cm}\] and \[\text{6 cm}\] long respectively.                    
    Based on the above information, answer the following questions,
          Find the area swept by the minute hand in 10 minutes.

    A) \[\text{22}.\text{24 c}{{\text{m}}^{\text{2}}}\]

    B) \[\text{42}.\text{42 c}{{\text{m}}^{\text{2}}}\]

    C) \[\text{44 c}{{\text{m}}^{\text{2}}}\]

    D) \[\text{44}\text{.42 c}{{\text{m}}^{\text{2}}}\]

    Correct Answer: B

    Solution :

    [b] Angles made by minutes hand in 60 minutes \[=360{}^\circ \]
    \[\therefore \] Area made by minute hand in 10 minutes
    \[=\frac{360{}^\circ }{60}\times 10=60{}^\circ \]
    Length of minute hand \[=9cm\]
    \[\therefore \] Area swept by minute hand in 10 minutes
    = Area of sector having central angles \[60{}^\circ \]
    \[=\pi {{r}^{2}}\left( \frac{60{}^\circ }{360{}^\circ } \right)=\frac{22}{7}\times 9\times 9\times \frac{1}{6}=\frac{297}{7}\]

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