The area of a sector formed by a $12\,cm$ long arc in a circle with radius $12\,cm$ is $\ldots \ldots \ldots \, cm^{2}$.

The area of $\odot(O, r)$ is $240 \, cm^2$. In $\odot(O, r)$,minor arc $\widehat{ACB}$ subtends an angle of measure $45^\circ$ at the centre. Then,the area of minor sector $OACB$ is $\dots \dots \dots \, cm^2$.

Is the area of the largest circle that can be drawn inside a rectangle of length $a \, cm$ and breadth $b \, cm$ $(a > b)$ equal to $\pi b^{2} \, cm^{2}$? Why?

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 $\ldots \ldots \ldots \,cm^{2}$.

The diameters of front and rear wheels of a tractor are $80 \,cm$ and $2 \,m$ respectively. Find the number of revolutions that the rear wheel will make in covering a distance in which the front wheel makes $1400$ revolutions.

The ratio of radii of two circles is $2:3$ and the ratio of the angles at the centre of two minor sectors of those circles is $5:2$. Then,the ratio of the areas of those sectors is: