Nine circular designs are made in a square show-piece as shown in the diagram. If the radius of each circle is $21\, cm$,find the area of the region without design. (in $cm^2$)

The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true? Why?

In the figure, a circle of radius $7.5 \, cm$ is inscribed in a square. Find the area of the shaded region (Use $\pi = 3.14$) (in $cm^2$).

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 $\odot(O, 7),$ the length of $\widehat{ABC}$ is $14.$ Then,$\ldots \ldots$ holds good.

In a circle with radius $14 \, cm$,$\overline{OA}$ and $\overline{OB}$ are radii perpendicular to each other. Then,the area of the minor sector corresponding to $\angle AOB$ is $\ldots \ldots \ldots \, cm^2$.