From each corner of a square of side $4\, cm$,a quadrant of a circle of radius $1\, cm$ is cut and also a circle of diameter $2\, cm$ is cut as shown in the figure. Find the area of the remaining portion of the square. [Use $\pi = \frac{22}{7}$]

(N/A) $1$. Area of the square $= (\text{side})^2 = (4\, cm)^2 = 16\, cm^2$.
$2$. Area of each quadrant of a circle with radius $r = 1\, cm$ is $\frac{1}{4} \pi r^2 = \frac{1}{4} \times \frac{22}{7} \times (1)^2 = \frac{22}{28} = \frac{11}{14}\, cm^2$.
$3$. Total area of $4$ quadrants $= 4 \times \frac{11}{14} = \frac{22}{7}\, cm^2$.
$4$. Area of the central circle with diameter $2\, cm$ (radius $r = 1\, cm$) $= \pi r^2 = \frac{22}{7} \times (1)^2 = \frac{22}{7}\, cm^2$.
$5$. Area of the remaining portion $= \text{Area of square} - (\text{Total area of } 4 \text{ quadrants} + \text{Area of central circle})$.
$6$. Area $= 16 - (\frac{22}{7} + \frac{22}{7}) = 16 - \frac{44}{7} = \frac{112 - 44}{7} = \frac{68}{7}\, cm^2$.