The ratio of radii of two circles is $2:3$ and the ratio of the angles at the centre of two minor sectors of those circles is $5:2$. Then,the ratio of the areas of those sectors is:

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 $\ldots \ldots \ldots \, cm^2$.

On a square handkerchief,nine circular designs each of radius $7\, cm$ are made (see figure). Find the area of the remaining portion of the handkerchief. (in $cm^2$) $\left[\right.$ Use $\left.\pi=\frac{22}{7}\right]$

The diameter of a circular garden is $210 \,m$. Inside it,all along the boundary,there is a path of uniform width $7 \,m$. Then,the area of the path is $\ldots \ldots \ldots \ldots \,m^2$.

If $\theta$ is the angle (in degrees) of a sector of a circle of radius $r$,then the area of the sector is:

In a circle,the area of a sector formed by two radii perpendicular to each other is $38.5 \, cm^2$. Find the radius of the circle (in $cm$).