| PQRS is the diameter of a circle of radius 6 cm. The length PQ, QR and RS are equal. Semi circles are drawn with PQ and QS as diameter as shown in the figure. The ratio of the area of the shaded region to that of the unshaded region is: |
 |
A) \[1:2\]
B) \[13:5\]
C) \[5:13\]
D) \[18:5\]
Correct Answer: A
Solution :
| [a] We have, \[PS=6\times 2=12cm\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,PQ=QR=RS=\frac{12}{3}=4cm\] |
| \[QS=QR+RS=4+4=8\,cm\] |
| Area of shaded part = Area of semicircle on PS- Area of semicircle on QS + Area of semicircle on PQ. |
| \[=\frac{1}{2}\pi {{(6)}^{2}}-\frac{1}{2}\pi {{(4)}^{2}}+\frac{1}{2}\pi {{(2)}^{2}}\] |
| \[=18\pi -8\pi +2\pi =12\pi c{{m}^{2}}\] |
| Area of unshaded part = Area of circle of radius 6 cm |
| = Area of shaded part |
| \[=\pi {{(6)}^{2}}-12\pi =24\pi c{{m}^{2}}\] |
| \[\therefore \] Required ratio \[=12\pi :24\pi =1:2\] |
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