question_answer

A square ABCD is inscribed in a circle of unit radius. Semicircles are described on each side as a diameter. The area of the region bounded by the four semicircles and the circle is

A)  1 sq unit          

B)  2 sq unit

C)  1.5 sq unit       

D)              2.5 sq unit

Correct Answer: B

Solution :

According to the question, Area of circle \[=\pi {{(1)}^{2}}=\pi \]sq unit Side of square ABCD \[=\frac{d}{\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}\]unit \[\therefore \]Area of square ABCD\[={{(\sqrt{2})}^{2}}=2\]sq unit Area of semicircle ABN \[=\frac{1}{2}\pi {{\left( \frac{1}{\sqrt{2}} \right)}^{2}}\] \[=\frac{\pi }{4}\]sq unit Hence, the required area sq unit