As shown in the diagram, the length of square $A B C D$ is $21\, cm .$ $\widehat{ A P C }$ is an arc of $\odot(B, BA )$ and $\widehat{A Q C}$ is an arc of $\odot( D , DA ) .$ Find the area of the shaded (ruled) portion. (in $cm^2$)
$265$
$186$
$248$
$252$
$\widehat{ ACB }$ is a minor arc of $\odot( O , 8 \,cm ) .$ If $m \angle AOB =45,$ the length of minor $\widehat{ ACB }$ is $\ldots \ldots \ldots . . cm .$
The area of a square inscribed in a circle with radius $70 \,cm$ is $\ldots \ldots \ldots cm ^{2}$.
The formula to find the length of a major arc of a circle is ............
A field is in the shape of an equilateral triangle in which the length of each side is $70\, m$. A cow is tethered at one of its vertices by a $5 \,m$ long rope. Find the area of the region in the field in which the cow can graze. $(\pi=3.14)$ (in $m^2$)
Floor of a room is of dimensions $5 \,m \times 4 \,m$ and it is covered with circular tiles of diameters $50 \,cm$ each as shown in $Fig.$ Find the area of floor that remains uncovered with tiles. (Use $\pi=3.14)$ (in $m ^{2}$)