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

As shown in the diagram,$\triangle ABC$ is an equilateral triangle in which $BC = 70 \, cm$ and $P$ and $R$ are midpoints of $\overline{AB}$ and $\overline{AC}$ respectively. $\widehat{PQR}$ is an arc of $\odot(A, AP)$. Find the area of the shaded region. $(\sqrt{3} = 1.73)$ (in $cm^2$)

$A$ wire fence is to be put up all around a circular ground with diameter $105 \, m$. The length of the fence is $\ldots \ldots \ldots \ldots \, m$.

In a circle with radius $42\,cm$,an arc subtends an angle of measure $120^{\circ}$ at the centre. Then,the area of the minor sector formed by that arc is $\ldots \ldots \ldots \,cm^{2}$.

In a circle with radius $6 \, cm$,the area of a sector corresponding to an arc of length $12 \, cm$ is $\ldots \ldots \ldots \, cm^2$.

Find the area of the shaded field shown in the figure.