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 length of a square field is $50 \, m$. $A$ cow is tethered at one of the vertices by a $3 \, m$ long rope. Find the area of the region of the field in which the cow can graze. $(\pi = 3.14)$ (in $m^2$)

In a circle with radius $6.3\, cm$,a minor arc subtends an angle of measure $40^{\circ}$ at the centre. The area of the minor sector corresponding to that arc is $\ldots \ldots cm^{2}$.

Find the circumference and the area of a circle with diameter $42 \, cm$.

In $\odot(O, 12)$, minor $\widehat{ACB}$ subtends an angle of measure $30^{\circ}$ at the centre. Then, the length of major $\widehat{ADB}$ is $\ldots \ldots \ldots \text{ cm}$. (in $\pi$)

In a circle with radius $7 \, cm$,the perimeter of a minor sector is $\frac{86}{3} \, cm$. Then,the area of that minor sector is $\ldots \ldots \ldots \ldots cm^2$.