| In the given figure, sectors of two concentric circles of radii 7 cm and 3.5 cm are shown, then the area of the shaded region is |
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A) \[96.25\text{ }c{{m}^{2}}\]
B) \[88.2\text{ }c{{m}^{2}}\]
C) \[9.625\text{ }c{{m}^{2}}\]
D) \[8.42\text{ }c{{m}^{2}}\]
Correct Answer: C
Solution :
Area of shaded region = (Area of sector having r = 7 cm,\[\theta =30{}^\circ \]) - (Area of sector having \[r=3.5=\frac{7}{2}cm,\,\theta =30{}^\circ \]) \[=\left[ \frac{22}{7}\times {{\left( 7 \right)}^{2}}\times \frac{30{}^\circ }{360{}^\circ } \right]-\left[ \frac{22}{7}\times {{\left( \frac{7}{2} \right)}^{2}}\times \frac{30{}^\circ }{360{}^\circ } \right]\] \[\left[ \because \,\,area\,of\,a\,\sec tor\,=\frac{\theta }{360{}^\circ }\times \pi {{r}^{2}} \right]\] \[=\left( \frac{77}{6}-\frac{77}{24} \right)=\frac{308-77}{24}\] \[=\frac{231}{24}=\frac{77}{8}=9.625\,c{{m}^{2}}\]
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