An archery target has three regions formed by three concentric circles as shown in the figure. If the diameters of the concentric circles are in the ratio $1: 2: 3$,then find the ratio of the areas of the three regions.

With the vertices $A, B$ and $C$ of a triangle $ABC$ as centres,arcs are drawn with radii $5 \, cm$ each as shown in the figure. If $AB = 14 \, cm, BC = 48 \, cm$ and $CA = 50 \, cm$,then find the area of the shaded region. (Use $\pi = 3.14$) (in $cm^2$)

In a circle with radius $14 \, cm$,$\overline{OA}$ and $\overline{OB}$ are radii perpendicular to each other. Then,the area of the minor sector corresponding to $\angle AOB$ is $\ldots \ldots \ldots \, cm^2$.

The radius of a circular ground is $35 \, m$. Inside it,a $3.5 \, m$ broad road runs around its boundary. $A$ part of the road between two radii forming an angle of measure $72^{\circ}$ at the centre is to be repaired. Find the cost of repairing at the rate of ₹ $80 / m^{2}$. (in ₹)

$A$ circular pond has a diameter of $17.5 \, m$. It is surrounded by a $2 \, m$ wide path. Find the cost of constructing the path at the rate of $Rs. \, 25$ per $m^2$ (in $Rs.$).

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