• # 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) $\text{44}\text{.42 c}{{\text{m}}^{\text{2}}}$

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 $60{}^\circ$ $=\pi {{r}^{2}}\left( \frac{60{}^\circ }{360{}^\circ } \right)=\frac{22}{7}\times 9\times 9\times \frac{1}{6}=\frac{297}{7}$ $=42.42c{{m}^{2}}$

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