A) \[2:\pi \]
B) \[\pi :2\]
C) \[\pi :4\]
D) \[4:\pi \]
Correct Answer: B
Solution :
[b] Let the side of square be 'a' units and the radius of circle be 'r' units. |
In right-angled \[\Delta ABC,\] |
\[A{{C}^{2}}=B{{C}^{2}}+A{{B}^{2}}\] |
(By Pythagoras theorem) |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,{{(2r)}^{2}}={{a}^{2}}+{{a}^{2}}\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,4{{r}^{2}}=2{{a}^{2}}\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,2{{r}^{2}}={{a}^{2}}\] |
Now, \[\frac{\text{Area of circle}}{\text{Area of square}}=\frac{\pi {{r}^{2}}}{{{a}^{2}}}=\frac{\pi {{r}^{2}}}{2{{r}^{2}}}=\frac{\pi }{2}\] |
Hence, the required ratio is \[\pi :2\]. |
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