| In the given figure, the ratio of the areas of two sectors \[{{S}_{1}}\] and \[{{S}_{2}}\] is: |
 |
A) \[5:2\]
B) \[3:5\]
C) \[5:3\]
D) \[4:5\]
Correct Answer: D
Solution :
| [d] Let r be the radius of the circle. |
| \[\therefore \]Area of the sector is given by \[\frac{\theta }{360{}^\circ }\times \pi {{r}^{2}}.\] |
| Area of sector \[{{S}_{1}}=\frac{120{}^\circ }{360{}^\circ }(\pi {{r}^{2}})=\frac{\pi {{r}^{2}}}{3}\] |
| Are of sector \[{{S}_{2}}=\frac{150{}^\circ }{360{}^\circ }(\pi {{r}^{2}})=\frac{5\pi {{r}^{2}}}{12}\] |
| \[\therefore \] Required ratio \[=\frac{\pi {{r}^{2}}}{3}:\frac{5\pi {{r}^{2}}}{12}=4:5\] |
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