As shown in the diagram, the radil of two concentric circles are $21\, cm$ and $28 \,cm .$ If $m \angle AOB =40,$ find the area of the shaded region. (in $cm^2$)
$125.65$
$175.36$
$119.78$
$114.46$
Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii $15 \,cm$ and $18 \,cm$ (in $cm$)
In a circle with radius $20 \,cm$, the measures of the angle subtended at the centre for two distinct sectors are $15$ and $90 .$ Then, the ratio of the areas of those sectors is $\ldots \ldots \ldots .$
In a circle with radius $14\,cm , \overline{ OA }$ and $\overline{ OB }$ are radii perpendicular to each other. Then, the area of the minor sector corresponding to $\angle AOB$ is $\ldots \ldots \ldots . cm ^{2}$.
Is it true that the distance travelled by a circular wheel of diameter $d\, cm$ in one revolution is $2 \pi d\, cm ?$ Why?
It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16\, m$ and $12 \,m$ in a locality. The radius of the new park would be (in $m$)