The length of the minute hand of a clock is $17.5\, cm$. Find the area of the region swept by it in $15$ minutes time duration. (in $cm^2$)

$\widehat{ACB}$ is a minor arc of $\odot(O, 8 \, cm)$. If $m\angle AOB = 45^\circ$, the length of minor $\widehat{ACB}$ is $\dots \, cm$. (in $\pi$)

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 $\ldots \ldots \ldots \ldots \,m^2$.

$A$ calf is tied with a rope of length $6 \,m$ at the corner of a square grassy lawn of side $20 \,m$. If the length of the rope is increased by $5.5 \,m$,find the increase in area of the grassy lawn in which the calf can graze. (in $m^2$)

In a circle with radius $14 \,cm$,an arc subtends a right angle at the centre. Find the length of this arc,the area of the minor sector,and the area of the minor segment formed by it.

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 $\ldots \ldots \ldots$.