question_answer

ABCD is a square. A circle is inscribed in the square. Also taking A, B, C, D (the vertices of square) as the centers, four Quadrants are drawn, which are touching each other on the mid-point of the sides of square. If the Area of square is 4 cm 2, what is the area of the shaded region?

A)  \[\left( 4-\frac{3\pi }{2} \right)c{{m}^{2}}\]      

B)  \[(2\pi -4)c{{m}^{2}}\]

C)  \[(4-2\pi )c{{m}^{2}}\]           

D)  \[\left( \frac{7-3\pi }{2} \right)c{{m}^{2}}\]

Correct Answer: B

Solution :

(b): Area of region x = Area of square ? Area of inscribed circle \[=(4-\pi )\]               Area of region y = Area of square ? 4(area of quadrant) \[=4-4\left( \frac{1}{4}\pi \times {{(1)}^{2}} \right)=(4-\pi )\] Required area (of shaded region) = Area of square ? {Area of region x + Area of region y] \[=4-[4-\pi +4-\pi ]=2\pi -4\]