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 $cm$)

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 $\pi = \frac{22}{7}$]

$AB$ and $CD$ are respectively arcs of two concentric circles of radii $21\, cm$ and $7\, cm$ with centre $O$ (see figure). If $\angle AOB = 30^{\circ}$,find the area of the shaded region.

In $\odot(O, r)$,chord $\overline{AB}$ subtends a right angle at the centre. The area of the minor segment $\overline{AB} \cup \widehat{ACB}$ is $114 \, cm^2$ and the area of $\Delta OAB$ is $200 \, cm^2$. Then,the area of the minor sector $OACB$ is ......... $cm^2$.

The length of the minute hand of a clock is $12\,cm$. The area of the region swept by it in $5$ minutes is $\ldots \ldots \ldots \,cm^2$. $(\pi=3.14)$

The radii of two concentric circles are $23 \, cm$ and $16 \, cm$. Find the area of the circular ring formed by the circles (in $cm^2$).