A) \[22:7\]
B) \[14:11\]
C) \[7:22\]
D) \[11:14\]
Correct Answer: B
Solution :
| [b] Let radius of a circle be r and side of a square be a. |
| Perimeter of a circle = Perimeter of a square |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,2\pi r=4a\,\,\,\Rightarrow \,\,\,a=\frac{\pi r}{2}\]...(1) |
| Now, \[\frac{\text{Area of a circle}}{\text{Area of a square}}=\frac{\pi {{r}^{2}}}{{{(a)}^{2}}}=\frac{\pi {{r}^{2}}}{{{\left( \frac{\pi r}{2} \right)}^{2}}}\] |
| [From eq.(1)] |
| \[=\frac{\pi {{r}^{2}}}{{{\pi }^{2}}{{r}^{2}}/4}=\frac{4}{\pi }=\frac{4}{22/7}=\frac{28}{22}=\frac{14}{11}\] |
| \[\therefore \] Required ratio \[=14:11\] |
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