Question

In the following figure, $\square ABCD$ is a square with side $CD$ as a diameter of the circle centred at $O$. If the area of the square is $100$ sq. units, calculate the area of the shaded region.

• A. $25\pi$ sq. units
• B. $50\pi$ sq. units
• C. $100\pi$ sq. units
• D. $\frac{25\pi }{2}$ sq. units

Answer 1

The correct option is D $\frac{25\pi }{2}$ sq. units

Area of the square $ABCD=$ side${}^2$

$\Rightarrow$ side${}^2=100$

$\Rightarrow$ side $=\sqrt{100}$

$\Rightarrow$ side $=10$ $cm$

$\therefore CD=10$ $cm$

$CD$ is the diameter of the circle ,so the radius of circle $=5$ $cm$.

Area of the circle $=$ $\pi r^2$

$\therefore$ Area of the shaded region $=$ $\frac{\pi r^2}{2}=\frac{\pi 5^2}{2}=\frac{25\pi }{2}$ sq. units