A) \[623.45\,\,c{{m}^{2}}\]
B) \[895.45\,\,c{{m}^{2}}\]
C) \[795.45\,\,c{{m}^{2}}\]
D) \[525.25\,\,c{{m}^{2}}\]
E) None of these
Correct Answer: C
Solution :
Perimeter of the rectangle = 2(20 + 30) = 100 cm According to the question, Perimeter of the circle = 100 cm or, \[2\pi r=100\] or,\[r=100\times \frac{7}{22}\times \frac{1}{2}\] Hence area of the circle\[=\pi {{r}^{2}}\] \[=\frac{22}{7}\times {{\left( \frac{100\times 7}{22\times 2} \right)}^{2}}\] \[=\frac{22}{7}\times \frac{100\times 100\times 7\times 7}{22\times 22\times 2\times 2}\] \[=\frac{25\times 7\times 50}{11}=795.45\,\,c{{m}^{2}}\]
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