A) \[\frac{2a}{\pi }c{{m}^{2}}\]
B) \[\frac{3a}{\pi }\,c{{m}^{2}}\]
C) \[\frac{4a}{\pi }\,c{{m}^{2}}\]
D) \[\frac{a}{\pi }\,c{{m}^{2}}\]
Correct Answer: C
Solution :
Area of the square \[=a\] Side of the square \[=\sqrt{Area}=\sqrt{a}\] \[\therefore \] Perimeter of the square \[=4\sqrt{a}\] Given, circumference of the circle = Perimeter of the square \[\Rightarrow \] \[2\pi r=4\sqrt{a}\] \[\therefore \] Radius of circle \[(r)=\frac{4\sqrt{a}}{2\pi }=\frac{2\sqrt{a}}{\pi }\] \[\therefore \] Area of circle \[=\pi {{r}^{2}}=\pi \,\left( \frac{2\sqrt{a}}{\pi } \right)=\frac{4a}{\pi }\,c{{m}^{2}}\]
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