| If area of a square is 64 sq cm, then the area of the circle formed by the same perimeter is |
A) \[\frac{215}{\pi }c{{m}^{2}}\]
B) \[\frac{216}{\pi }c{{m}^{2}}\]
C) \[\frac{256}{\pi }c{{m}^{2}}\]
D) \[\frac{318}{\pi }c{{m}^{2}}\]
Correct Answer: C
Solution :
| Area of square \[=64\,\,c{{m}^{2}}\] |
| \[{{\text{(Side)}}^{2}}=64\] [a = side] |
| \[\therefore \] \[\text{Side}=\sqrt{64}=8\,\,cm\] |
| According to the question, |
| \[\Rightarrow \] \[2\pi r=4\times 8\] |
| \[\Rightarrow \] \[r=\frac{4\times 8}{2\pi }=\frac{16}{\pi }\] |
| \[\therefore \]Area of the circle \[=\pi \times \frac{16}{\pi }\times \frac{16}{\pi }=\frac{256}{\pi }\,\,c{{m}^{2}}\] |
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