In $Fig.$ $ABCD$ is a trapezium with $AB \| DC , AB =18 \,cm , DC =32 \,cm$ and distance between $AB$ and $DC =14\, cm .$ If arcs of equal radii $7\, cm$ with centres $A , B , C$ and $D$ have been drawn, then find the area of the shaded region of the figure. (in $cm^2$)

The length of the minute hand of a clock is $6\,cm .$ The area of the region swept by it in $10$ minutes is $\ldots \ldots \ldots \ldots cm ^{2}$.  $(\pi=3.14)$

In a circle with radius $30\,cm ,$ a minor arc subtends an angle of measure $60$ at the centre. Then, the area of the minor sector formed by that arc is $\ldots \ldots \ldots \ldots$ $cm ^{2}$.   $(\pi=3.14)$

In a circle with radius $14 \,cm ,$ the area of minor sector corresponding to minor $\widehat{ ACB }$ is $77 \,cm ^{2}$. Then, minor $\widehat{ ACB }$ subtends an angle of measure $\ldots \ldots \ldots \ldots$ at the centre.

Floor of a room is of dimensions $5 \,m \times 4 \,m$ and it is covered with circular tiles of diameters $50 \,cm$ each as shown in $Fig.$ Find the area of floor that remains uncovered with tiles. (Use $\pi=3.14)$ (in $m ^{2}$)

In $\odot( O , 6), \widehat{ ABC }$ is a major arc and $m \angle AOC =60 .$ Then, the length of major $\widehat{ ABC }$ is ...........