SATHEE: Quantitative Aptitude Ques 2087

Quantitative Aptitude Ques 2087

Question: 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

Options:

A) $ 16\frac{2}{7} $

B) $ 18\frac{2}{7} $

C) $ 10\frac{2}{7} $

D) $ 12\frac{2}{7} $

Show Answer

Answer:

Correct Answer: B

Solution:

Let side of square be x. $ x^{2}+x^{2}=8^{2} $

$ \Rightarrow $ $ 2x^{2}=64 $
$ \Rightarrow $ $ x^{2}=\frac{64}{2} $
$ \Rightarrow $ $ x=\frac{8}{\sqrt{2}} $

$ \therefore $ Area of circle $ =\frac{22}{7}\times {{( \frac{8}{2} )}^{2}}cm^{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}cm^{2} $

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