In a circle with radius $21 \ cm$,the perimeter of a minor sector is $64 \ cm$. Then,the length of the arc of that sector is $\ldots \ cm$.

In the given figure,$OACB$ is a quadrant of a circle with centre $O$ and radius $3.5 \, cm$. If $OD = 2 \, cm$,find the area of the:
$(i)$ quadrant $OACB$,
$(ii)$ shaded region. $\left[ \text{Use } \pi = \frac{22}{7} \right]$

In a circle with radius $6.3\, cm$,a minor arc subtends an angle of measure $40^{\circ}$ at the centre. The area of the minor sector corresponding to that arc is $\ldots \ldots cm^{2}$.

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

The maximum area of a triangle inscribed in a semicircle with diameter $30 \, cm$ is $\ldots \ldots \ldots \, cm^{2}$.

In $\odot(O, r)$,minor arc $\widehat{ABC}$ subtends a right angle at the centre. The area of the minor segment formed by $\widehat{ABC}$ is $14.25\,cm^2$ and the area of $\Delta OAC$ is $25\,cm^2$. Then,the area of the minor sector formed by $\widehat{ABC}$ is $\ldots \ldots \ldots cm^2$.