Question

The figure shows nine 1cm $\times$ 1 cm squares and a circe. The circle passes through the centres of the squares in the four corners.

What is the area (in sq. cm) of the shaded region?

• A. $81-\sqrt{2}\pi$
• B. $\frac{9-2\pi }{4}$
• C. $9-2\pi$
• D. $\frac{81-2\pi }{2}$

Answer 1

The correct option is B $\frac{9-2\pi }{4}$

Area of square = 9sq cm
area of circle =$\pi r^2$ =$\pi \times {\left(\sqrt{2}\right)}^2=2\pi sqcm$ (two diagonals of in smaller squares make the diameter on the circle)
area of the shaded region =$\frac{(9-2\pi )}{4}cm$