| In the figure, PQRS is a square, O is centre of the circle. If \[RS=10\sqrt{2}\,cm,\] then area of shaded region is: |
 |
A) \[(90\pi -90)c{{m}^{2}}\]
B) \[(80\pi -80)c{{m}^{2}}\]
C) \[(50\pi -100)c{{m}^{2}}\]
D) \[(100\pi -100)c{{m}^{2}}\]
Correct Answer: C
Solution :
| [c] Diagonal of square |
| \[=\sqrt{2}\,\,(side)=\sqrt{2}\times (10\sqrt{2})\] |
| \[=20cm\] |
| \[\therefore \] Diameter of circle \[=20cm\] |
| \[\therefore \] Radius of circle \[(r)=\frac{20}{2}=10cm\] |
| Area of circle \[=\pi {{r}^{2}}=\pi \times {{(10)}^{2}}=100\pi c{{m}^{2}}\] |
| Area of square \[={{(side)}^{2}}={{(10\sqrt{2})}^{2}}=200c{{m}^{2}}\] |
| Area of circle not included in the square |
| \[=(100\pi -200)c{{m}^{2}}\] |
| \[\therefore \] Area of shaded portion \[=\frac{1}{2}(100\pi -200)\] |
| \[=(50\pi -100)c{{m}^{2}}\] |
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