Question

The area of the shaded region in the given figure is

• A. 4π sq. units
• B. 16-16π sq. units
• C. 16-4π sq. units
• D. None of these

Answer 1

The Correct Option is C

The figure shows a circle inscribed in a square $OBA$ with radius $r = 4$. 

Let the vertex of the square be $C$. Since $OBA$ forms a square with $OA=OB=4$, the side of the square $ABOC$ is also 4. 

The area of the square is $4^2 = 16$. 

The area of the quarter circle $OAB$ is $\frac{1}{4} \pi r^2 = \frac{1}{4} \pi (4^2) = \frac{1}{4} \pi (16) = 4\pi$. 

The area of the shaded region is the area of the square minus the area of the quarter circle. 

Area of shaded region = Area of square $ABOC$ - Area of quarter circle $OAB$ $= 16 - 4\pi$ sq. units.