Find the difference of the areas of a sector of angle $120^{\circ}$ and its corresponding major sector of a circle of radius $21 \, cm$. (in $cm^2$)

Find the area of the sector of a circle of radius $5\, cm$,if the corresponding arc length is $3.5\, cm$. (in $cm^2$)

In the adjoining diagram, $\overline{ AB }$ and $\overline{ CD }$ are diameters of $\odot( O , 7\, cm )$ perpendicular to each other. $A$ circle is drawn with diameter $\overline{ OD }$. Find the area of the shaded region. (in $cm^2$)

Two minor sectors of two distinct circles have the measure of the angle at the centre equal. If the ratio of their areas is $4:9,$ then the ratio of the radii of the circles is ........

Points $A$ and $B$ are distinct points on $\odot(O, r)$ and point $C$ on the circle lies in the interior of $\angle AOB$. Then,$\overline{AB} \cup \widehat{ACB}$ is ........

If the radius of a circle is increased by $10 \%,$ its area will increase by $\ldots \ldots \ldots . \%$