question_answer

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 \[=\frac{352}{7}-32\]

\[=\frac{352-224}{7}=\frac{128}{7}=18\frac{2}{7}c{{m}^{2}}\]