The maximum area of $\Delta ABC$ inscribed in a semicircle with radius $10 \, cm$ is ....... $cm^2$.

As shown in the diagram,the radii of two concentric circles are $21 \, cm$ and $28 \, cm$. If $m \angle AOB = 40^\circ$,find the area of the shaded region. (in $cm^2$)

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 diameter of a circle whose area is equal to the sum of the areas of the two circles of radii $24 \, cm$ and $7 \, cm$ is (in $cm$):

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 $\text{cm}^2$.

$A$ running track is in the shape of a circular ring. The difference of its outer circumference and inner circumference is $44\,m$. Then,the width of the track is $\ldots \ldots \ldots \ldots\,m$.