In a circle,the length of a minor arc is $110 \,cm$ and it subtends an angle of measure $150^{\circ}$ at the centre. Then,the radius of the circle is $\ldots \ldots \ldots \ldots \,cm$.

$A$ chord of a circle of radius $12 \, cm$ subtends an angle of $120^{\circ}$ at the centre. Find the area of the corresponding segment of the circle. (in $cm^2$)
(Use $\pi = 3.14$ and $\sqrt{3} = 1.73$)

In a circle with radius $42 \, cm$,an arc subtends an angle of $120^{\circ}$ at the centre. Find the length of this arc and the area of the sector formed by this arc.

If the sum of the areas of two circles with radii $R_{1}$ and $R_{2}$ is equal to the area of a circle of radius $R$,then

In a circle with radius $42\,cm$,an arc subtends an angle of measure $120^{\circ}$ at the centre. Then,the area of the minor sector formed by that arc is $\ldots \ldots \ldots \,cm^{2}$.

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