The area of a minor sector of $\odot(P, 30)$ is $300 \, cm^2$. The length of the arc corresponding to it is .......... $cm$.

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 ......... $cm^2$.

An umbrella has $8$ ribs which are equally spaced. Assuming the umbrella to be a flat circle with radius $56 \, cm$,the area between two consecutive ribs is $\ldots \ldots \ldots \, cm^{2}$.

In a circle,the ratio of the areas of two distinct minor sectors is $1:4$. Then,the ratio of the angles at the centre for those minor sectors is $\ldots \ldots \ldots \ldots$.

In a circle,the area of a sector formed by two radii perpendicular to each other is $38.5 \, cm^2$. Find the radius of the circle (in $cm$).

Is the following statement true? Give reasons for your answer.
Area of a segment of a circle $=$ area of the corresponding sector $-$ area of the corresponding triangle.