In $\odot(O, r)$,chord $\overline{AB}$ subtends a right angle at the centre. The area of the minor segment $\overline{AB} \cup \widehat{ACB}$ is $114 \, cm^2$ and the area of $\Delta OAB$ is $200 \, cm^2$. Then,the area of the minor sector $OACB$ is ......... $cm^2$.

In $\odot(O, r)$,minor $\widehat{ACB}$ subtends an angle of measure $72^{\circ}$ at the centre. Then,the ratio of the length of minor $\widehat{ACB}$ and the circumference of the circle is ............

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 $cm^2$).

The circumference of a circle is $251.2 \, cm$. Find its diameter. $(\pi = 3.14)$ (in $cm$)

In the given diagram,$\Delta ABC$ is a right-angled triangle in which $m \angle B = 90^{\circ}$ and $AB = BC = 14 \text{ cm}$. $A$ minor sector $BAPC$ is a sector of a circle with center $B$ and radius $BA$. $A$ semicircle arc $\widehat{AQC}$ is drawn on diameter $\overline{AC}$. Find the area of the shaded region in $\text{cm}^2$.

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