From a circular metallic sheet with radius $21\, cm$,a regular hexagon of side $21\, cm$ is cut off. Find the area of the remaining sheet. $(\sqrt{3} = 1.73)$ (in $cm^2$)

In a circle with radius $14 \,cm$,an arc subtends a right angle at the centre. Find the length of this arc,the area of the minor sector,and the area of the minor segment formed by it.

The length of the diagonals of a square garden $ABCD$ is $120\, m$. As shown in the figure,there are flower beds on two opposite sides of the garden in the shape of minor segments,the center of which is the point of intersection of the diagonals. Find the area of these flower beds. $(\pi=3.14)$ (in $m^2$)

The area of the circle that can be inscribed in a square of side $6 \, cm$ is (in $cm^2$) (in $\pi$)

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 $\text{cm}^2$)

The length of the minute hand of a clock is $12\,cm$. The area of the region swept by it in $5$ minutes is $\ldots \ldots \ldots \,cm^2$. $(\pi=3.14)$