A) \[\text{231 c}{{\text{m}}^{\text{2}}}\]
B) \[~\text{221 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{21}0\,\text{c}{{\text{m}}^{\text{3}}}\]
D) \[\text{2}00\,\text{c}{{\text{m}}^{\text{2}}}\]
Correct Answer: A
Solution :
The angle swept by the minute hand in 60 minutes\[3465={{3}^{2}}\times 5\times 7\times 11\] \[\text{546}0=\text{22}\times \text{3}\times \text{5}\times \text{7}\times \text{l3}\]The angle swept by the minute hand in 10 minutes\[\therefore \] \[={{2}^{2}}\times {{3}^{2}}\times 5\times 7\times 11\times 13=180180\]Sector angle\[\therefore \] The area swept by the minute hand in 10 minutes = The area of a sector of a circle of radius 21 cm and sector angle\[H.C.F.=\frac{\text{Product of the numbers}}{L.C.M.}\]. \[\text{5474}=\text{2}\times \text{7}\times \text{17}\times \text{23}\] \[\text{9775}={{\text{5}}^{\text{2}}}\times \text{17}\times \text{23}\]
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