The length of the diagonal of a square is 8 cm. A circle has been drawn circumscribing the square. The area of the portion between the circle and the square (in sq cm) is [SSC (FCI) 2012] |
A) \[16\frac{2}{7}\]
B) \[18\frac{2}{7}\]
C) \[10\frac{2}{7}\]
D) \[12\frac{2}{7}\]
Correct Answer: B
Solution :
Let side of square be x. |
\[{{x}^{2}}+{{x}^{2}}={{8}^{2}}\] |
\[\Rightarrow \]\[2{{x}^{2}}=64\]\[\Rightarrow \]\[{{x}^{2}}=\frac{64}{2}\]\[\Rightarrow \]\[x=\frac{8}{\sqrt{2}}\] |
\[\therefore \]Area of circle \[=\frac{22}{7}\times {{\left( \frac{8}{2} \right)}^{2}}c{{m}^{2}}\] |
\[=\frac{22}{7}\times 16=\frac{352}{7}\,\,cm\] |
\[\therefore \]Required difference \[=\frac{352}{7}-32\] |
\[=\frac{352-224}{7}=\frac{128}{7}=18\frac{2}{7}c{{m}^{2}}\] |
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