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 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 $cm$).

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 $\ldots \ldots \ldots \, cm^{2}$.

If the sum of the areas of two circles with radii $R_{1}$ and $R_{2}$ is equal to the area of a circle of radius $R$,then

In the figure,$ABC$ is a quadrant of a circle of radius $14 \, cm$ and a semicircle is drawn with $BC$ as diameter. Find the area of the shaded region. (in $cm^2$) [Use $\pi = \frac{22}{7}$]

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 $\text{cm}^2$)