The radii of two circles are $19\, cm$ and $9\, cm$ respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles. (in $cm$) [use $\pi=\frac{22}{7}$]

In the given figure,$OACB$ is a quadrant of a circle with centre $O$ and radius $3.5 \, cm$. If $OD = 2 \, cm$,find the area of the:
$(i)$ quadrant $OACB$,
$(ii)$ shaded region. $\left[ \text{Use } \pi = \frac{22}{7} \right]$

Find the area of the shaded region in the figure if $ABCD$ is a square of side $14 \, cm$ and $APD$ and $BPC$ are semicircles. (in $cm^2$) [Use $\pi = \frac{22}{7}$]

Fig. depicts an archery target marked with its five scoring regions from the centre outwards as $Gold, Red, Blue, Black$ and $White.$ The $diameter$ of the region representing Gold score is $21\, cm$ and each of the other bands is $10.5 \,cm$ wide. Find the area of each of the five scoring regions. [use $\pi=\frac{22}{7}$]

Find the area of the segment $AYB$ shown in the figure if the radius of the circle is $21 \, cm$ and $\angle AOB = 120^{\circ}$. (Use $\pi = \frac{22}{7}$)

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 $\pi = 3.14$).