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