In a circle with radius $20 \,cm$,the measures of the angle subtended at the centre for two distinct sectors are $15^{\circ}$ and $90^{\circ}$. Then,the ratio of the areas of those sectors is $\ldots \ldots \ldots$.

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 ratio of the radii of two circles is $4: 5$. Then,the ratio of their areas is...........

In a circle with radius $r,$ an arc subtends an angle of measure $\theta$ at the centre. Then,the area of the major sector is $=$ ..........

Find the area of the minor segment of a circle of radius $14 \, cm$,when the angle of the corresponding sector is $60^{\circ}$. (in $cm^{2}$)

As shown in the adjoining diagram,the length of the side of the square plot $ABCD$ is $50 \, m$. At each vertex of the plot,a flower bed in the shape of a sector with radius $10 \, m$ is prepared. Find the area of the plot excluding the flower beds. $(\pi = 3.14)$ (in $m^2$)