Question

O is the centre of a circle of diameter $4$cm and OABC is a square, if the shaded area is $\frac{1}{3}$ area of the square, then the side of the square is __________.

• A. $\pi \sqrt{3}$cm
• B. $\sqrt{3\pi }$cm
• C. $3\sqrt{\pi }$cm
• D. $3\pi$cm

Answer 1

The correct option is B $\sqrt{3\pi }$cm

$O$ is the center of the circle and the diameter is $4$ units.

Also area of the shaded region$=\frac{1}{3}$ area of the square

Area of the shaded region $=\pi r^2\times \frac{90}{360}=\pi \left(4\right)\left(\frac{1}{4}\right)=\pi$

Area of the square $=a^2=\pi \times 3=3\pi$

$\therefore a=\sqrt{3\pi }$cm