In a circle with radius $20\, cm$,the area of a sector formed by an arc of length $10\, cm$ is ............. $cm^2$.

In the figure,$ABCD$ is a trapezium with $AB \parallel DC$,$AB = 18 \, cm$,$DC = 32 \, cm$,and the distance between $AB$ and $DC = 14 \, cm$. If arcs of equal radii $7 \, cm$ with centers $A, B, C$,and $D$ have been drawn,find the area of the shaded region of the figure (in $cm^2$).

In a circle of radius $21\, cm$,an arc subtends an angle of $60^{\circ}$ at the centre. Find:
$(i)$ the length of the arc
$(ii)$ area of the sector formed by the arc
$(iii)$ area of the segment formed by the corresponding chord [Use $\pi = \frac{22}{7}$]

The length of a minor arc of a circle is given by the formula $\ldots \ldots \ldots \ldots$

In a circle with radius $14 \,cm$,an arc subtends a right angle at the centre. Find the length of this arc,the area of the minor sector,and the area of the minor segment formed by it.

In a circle with radius $10 \, cm$,the area of a minor sector is $75 \, cm^2$. Then,the length of the arc of that sector is $\ldots \, cm$.