The length of the minute hand of a clock is $10.5 \, cm$. Find the area of the region swept by it between $2.25 \, PM$ and $2.40 \, PM$. (in $cm^2$)

As shown in the diagram,$\overline{AC}$ is a diameter of the circle with centre $O$. $\Delta ABC$ is inscribed in the circle. If $AC = 35 \, cm$,$AB = 21 \, cm$ and $BC = 28 \, cm$,find the area of the shaded region in $cm^2$.

If the radius of a circle is increased by $10 \%,$ then the corresponding area of the new circle will be $\ldots \ldots \ldots . . .$

Area of a sector of central angle $200^{\circ}$ of a circle is $770 \, cm^{2}$. Find the length of the corresponding arc of this sector. (in $cm$)

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

$\widehat{ACB}$ 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 $\pi$)