In $Fig.$,$ABCD$ is a square of side $14 \, cm$. With centres $A, B, C$ and $D$,four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region (in $cm^2$). $\left[\text{Use } \pi = \frac{22}{7}\right]$

To warn ships for underwater rocks,a lighthouse spreads a red coloured light over a sector of angle $80^{\circ}$ to a distance of $16.5 \, km$. Find the area of the sea over which the ships are warned. (in $km^2$) (Use $\pi=3.14$)

In the figure,$AB$ and $CD$ are two diameters of a circle (with centre $O$) perpendicular to each other. $OD$ is the diameter of the smaller circle. If $OA = 7 \, cm$,find the area of the shaded region in $cm^2$. [Use $\pi = \frac{22}{7}$]

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 $\left.\pi=\frac{22}{7}\right]$

In a circle of radius $21\, cm$,an arc subtends an angle of $60^{\circ}$ at the centre. Find:
$(i)$ the length of the arc
$(ii)$ area of the sector formed by the arc
$(iii)$ area of the segment formed by the corresponding chord [Use $\pi = \frac{22}{7}$]

The figure depicts a racing track whose left and right ends are semicircular.
The distance between the two inner parallel line segments is $60 \, m$ and they are each $106 \, m$ long. If the track is $10 \, m$ wide,find:
$(i)$ the distance around the track along its inner edge
$(ii)$ the area of the track. $\left[ \text{Use } \pi = \frac{22}{7} \right]$