The ratio of the areas of $\odot(O, 6)$ and $\odot(P, 12)$ is ...........

Is it true that the distance travelled by a circular wheel of diameter $d \text{ cm}$ in one revolution is $2 \pi d \text{ cm}$? Why?

In the given diagram,$\Delta ABC$ is a right-angled triangle in which $m \angle B = 90^{\circ}$ and $AB = BC = 14 \text{ cm}$. $A$ minor sector $BAPC$ is a sector of a circle with center $B$ and radius $BA$. $A$ semicircle arc $\widehat{AQC}$ is drawn on diameter $\overline{AC}$. Find the area of the shaded region in $\text{cm}^2$.

Sides of a triangular field are $15 \, m$,$16 \, m$,and $17 \, m$. At the three corners of the field,a cow,a buffalo,and a horse are tied separately with ropes of length $7 \, m$ each to graze in the field. Find the area of the field which cannot be grazed by the three animals.

In the figure,a square is inscribed in a circle of diameter $d$ and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

If the circumference of a circle and the perimeter of a square are equal,then