A) \[161\text{ }c{{m}^{2}}\]
B) \[166\text{ }c{{m}^{2}}\]
C) \[\text{616 }c{{m}^{2}}\]
D) \[\text{916 }c{{m}^{2}}\]
E) None of these
Correct Answer: C
Solution :
Explanation \[\operatorname{Area} of square = 484 c{{m}^{2}}\] \[\operatorname{Side}\,\,of\,\,square=\,\,\sqrt{484}\,\,=\,\,22cm\] \[\operatorname{Perimetre} of square = 4 \times 22 cm = 88 cm\] Let r be the radius of the circle. Same wire is bent in the form of a square and circle. Therefore, circumference of the circle = perimetre of the square. or \[2\pi r = 88\] \[2\times \frac{22}{7} \times r = 88 \,\Rightarrow \,r = \frac{88\times 7}{2\times 22} = 14 cm\] Thus area of circle \[= \,\pi {{r}^{2}}\,\,=\,\,\frac{22}{7} \times 14 \times 14 = 616 c{{m}^{2}}.\]
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