In a circle with radius $20\, cm$,the area of a sector formed by an arc of length $10\, cm$ is ............. $cm^2$.

The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true? Why?

The side length of square $ABCD$ is $14 \, cm$. As shown in the diagram,circles with radius $7 \, cm$ are drawn with each vertex as the centre so that each circle touches two other circles externally. Find the area of the shaded region in $cm^2$.

An umbrella has $8$ ribs which are equally spaced. Assuming the umbrella to be a flat circle with radius $56 \, cm$,the area between two consecutive ribs is $\ldots \ldots \ldots \, cm^{2}$.

From a circular metallic sheet with radius $21\, cm$,a regular hexagon of side $21\, cm$ is cut off. Find the area of the remaining sheet. $(\sqrt{3} = 1.73)$ (in $cm^2$)

$A$ running track is in the shape of a circular ring. The difference of its outer circumference and inner circumference is $44\,m$. Then,the width of the track is $\ldots \ldots \ldots \ldots\,m$.