The ratio of the areas of the circles with radii $8 \, cm$ and $12 \, cm$ is $\ldots \ldots \ldots \ldots .$

The length of a square field is $50 \, m$. $A$ cow is tethered at one of the vertices by a $3 \, m$ long rope. Find the area of the region of the field in which the cow can graze. $(\pi = 3.14)$ (in $m^2$)

$\overline{ OA }$ and $\overline{ OB }$ are radii of a circle perpendicular to each other. If $OA = 5.6 \, cm$,then the area of the minor sector formed by those radii is .......... $cm^2$.

In the given diagram,the shaded portion represents a flower bed in a plot. If $m \angle O = 90^\circ$,$OB = 21 \, \text{m}$,and $OD = 14 \, \text{m}$,find the area of the flower bed in $\text{m}^2$.

In a circle with radius $8.4 \, cm$,a minor arc subtends an angle of $60^{\circ}$ at the centre. Find the area of the minor sector and the major sector corresponding to this arc.

Four circular cardboard pieces of radii $7 \, cm$ are placed on a paper in such a way that each piece touches the other two pieces. Find the area of the portion enclosed between these pieces (in $cm^2$).