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 $10.30 \, AM$.

Is the area of the largest circle that can be drawn inside a rectangle of length $a \, cm$ and breadth $b \, cm$ $(a > b)$ equal to $\pi b^{2} \, cm^{2}$? Why?

$A$ chord of a circle of radius $20\, cm$ subtends an angle of $90^{\circ}$ at the centre. Find the area of the corresponding major segment of the circle. (Use $\pi=3.14$) (in $cm^2$)

The area of $\odot(O, r)$ is $240 \, cm^2$. In $\odot(O, r)$,minor arc $\widehat{ACB}$ subtends an angle of measure $45^\circ$ at the centre. Then,the area of minor sector $OACB$ is $\dots \dots \dots \, cm^2$.

In $\odot(O, r)$,minor $\widehat{ACB}$ subtends an angle of measure $72^{\circ}$ at the centre. Then,the ratio of the length of minor $\widehat{ACB}$ and the circumference of the circle is ............

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