The length of the minute hand of a clock is $14 \, cm$. Find the area of the region swept by it between $10.10 \, AM$ to $10.30 \, AM$.

$A$ horse is tied to a peg at one corner of a square-shaped grass field of side $15 \, m$ by means of a $5 \, m$ long rope (see figure). Find:
$(i)$ The area of that part of the field in which the horse can graze.
$(ii)$ The increase in the grazing area if the rope were $10 \, m$ long instead of $5 \, m$. (Use $\pi = 3.14$)

In a circle with radius $6 \, cm$,a minor arc subtends an angle of measure $60^{\circ}$ at the centre. Find the area of the minor sector and the major sector corresponding to that arc.

$\overline{ OA }$ and $\overline{ OB }$ are radii of a circle perpendicular to each other. If $OA = 5.6 \, cm$,then the area of the minor sector formed by those radii is .......... $cm^2$.

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii $15 \, cm$ and $18 \, cm$ (in $cm$).

In $\odot(O, 4)$,$\widehat{ACB}$ is a minor arc and $m \angle AOB = 45^\circ$. Then,the length of minor $\widehat{ACB}$ is $\ldots \ldots \ldots \ldots$