Find the ratio of the area of the circle circumscribing a square to the area of the circle inscribed in the square.

Find the circumference of a circle whose area is $6.16 {\mathrm{cm}}^2$.

In the figure, $ABCD$ is a square of side $14 cm. A, B, C \& D$ are the canters of four congruent circles such that each circle touches extremely two of the remaining three circles. If the area of the shaded region is $k c{m}^2$ then find the value of $k$.

A CCTV camera is placed on the top of a $24$ m high pole in such a way that traffic can be seen beyond $25$ metre of line of sight of it. Find the area of the Green patch around the pole.

Find the area of shaded region in Fig.$4$, if $ABCD$ is a rectangle with sides $8 cm$ and $6cm$ and $O$ o is the centre of circle $\left(Take \pi =3.14\right)$

In a circle of radius $21$cm an arc subtends an angle of $60°$ at the centre. Find the length of the arc.

A hemispherical vessel of radius $14 cm$ is fully filled with sand. This sand is poured on level ground. The heap of sand forms a cone shape of height $7 cm$. If the area of ground occupied by the circular base of the heap of the sand is $k c{m}^2$, then find the value of $k$.

Let $AB$ be a sector of a circle with centre $O$ and radius $d.\angle AOB=\theta \left(<\frac{\pi }{2}\right)$ and $D$ be a point on $OA$ such that $BD$ is perpendicular$OA$. Let $E$ be the mid-point of $BD$ and $F$ be a point on the arc $AB$ such that $EF$ is parallel to $OA$. Then, the ratio of length of the arc$AF$ to the length of the arc $AB$ is