The diameter of a circle with area $38.5 \, m^2$ is $\ldots \ldots \ldots \ldots m$.

In $\odot(O, 6)$, $\widehat{ABC}$ is a major arc and $m \angle AOC = 60^{\circ}$. Then, the length of major $\widehat{ABC}$ is ........... (in $\pi$)

In a circle with centre $O$,$\overline{OA}$ and $\overline{OB}$ are radii perpendicular to each other. The perimeter of the sector formed by these radii is $75 \, cm$. Find the area of the corresponding minor segment. (in $cm^2$)

As shown in the diagram,$\overline{OA}$ and $\overline{OB}$ are two radii of $\odot(O, 35 \text{ cm})$ perpendicular to each other. If $OD = 12 \text{ cm}$,find the area of the shaded region. (in $\text{cm}^2$)

$A$ 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 $\pi = 3.14$)

$AB$ and $CD$ are respectively arcs of two concentric circles of radii $21\, cm$ and $7\, cm$ with centre $O$ (see figure). If $\angle AOB = 30^{\circ}$,find the area of the shaded region.