Question

Four equal circles describe the four corners of a square such that each touches two of the others. If each side of the square is $14cm$, then the area enclosed between the circumferences of the circle is:

• A. $24$ sq cm
• B. $42$ sq cm
• C. $154$ sq cm
• D. $196$ sq cm

Answer 1

The correct option is B $42$ sq cm

Given, side of the square $=14cm$
Therefore, radius of each circle $=7cm$
Now, area of each quadrant of circle $=\frac{\pi r^2}{4}$
Therefore, area of the four quadrants of the circle $=4\times \frac{\pi r^2}{4}=\pi r^2$
$=\frac{22}{7}\times {\left(7\right)}^2=154{cm}^2$
Also, area of square $=side\times side=14cm\times 14cm=196{cm}^2$
Now, area enclosed between the circumference of the circle $=196{cm}^2$ - $154{cm}^2$ = $42{cm}^2$