In $\odot(O, r)$,$\overline{OA}$ and $\overline{OB}$ are two radii perpendicular to each other. If the perimeter of the minor sector formed by these radii is $20\,cm$,then $r = \ldots\,cm$.

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 $cm^2$)

Find the diameter of the circle whose area is equal to the sum of the areas of the two circles of diameters $20 \, cm$ and $48 \, cm$. (in $cm$)

$\overline{ OA }$ and $\overline{ OB }$ are radii of a circle perpendicular to each other. If $OA = 5.6 \, cm$,then the area of the minor sector formed by those radii is .......... $cm^2$.

In the figure,arcs have been drawn with a radius of $21 \, cm$ each,using vertices $A, B, C,$ and $D$ of quadrilateral $ABCD$ as centers. Find the area of the shaded region in $cm^2$.

In a circle with radius $r,$ an arc subtends an angle of measure $\theta$ at the centre. Then,the area of the major sector is $=$ ..........