On a square handkerchief,nine circular designs each of radius $7\, cm$ are made (see figure). Find the area of the remaining portion of the handkerchief. (in $cm^2$) $\left[\right.$ Use $\left.\pi=\frac{22}{7}\right]$

$A$ horse is tied to a peg at one corner of a square-shaped grass field of side $15 \, m$ by means of a $5 \, m$ long rope (see figure). Find:
$(i)$ The area of that part of the field in which the horse can graze.
$(ii)$ The increase in the grazing area if the rope were $10 \, m$ long instead of $5 \, m$. (Use $\pi = 3.14$)

In the figure,two circular flower beds are shown on two sides of a square lawn $ABCD$ of side $56 \, m$. If the centre of each circular flower bed is the point of intersection $O$ of the diagonals of the square lawn,find the sum of the areas of the lawn and the flower beds (in $m^2$).

The radii of two circles are $8 \, cm$ and $6 \, cm$ respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles. [use $\pi = \frac{22}{7}$] (in $cm$)

Find the area of the shaded region in the figure,where $ABCD$ is a square of side $14 \, cm$. (in $cm^2$)

Find the area of the sector of a circle with radius $4\, cm$ and of angle $30^{\circ}$. Also,find the area of the corresponding major sector (in $cm^2$) (Use $\pi = 3.14$).