The area of a square inscribed in a circle of radius $35 \, cm$ is $\ldots \ldots \ldots \ldots cm^{2}$.

In a circle with radius $50 \, cm$,the area of the sector formed by a $20 \, cm$ long arc is $\ldots \ldots \ldots cm^2$.

As shown in the diagram,$\overline{ OA }$ and $\overline{ OB }$ are two radii of $\odot( O , 21 \text{ cm} )$ perpendicular to each other. If $OD = 10 \text{ cm}$,find the area of the shaded region. (in $\text{cm}^2$)

Is it true to say that the area of a segment of a circle is less than the area of its corresponding sector? Why?

The length of a minor arc of a circle is given by the formula $\ldots \ldots \ldots \ldots$

In $\odot(O, r)$,minor arc $\widehat{ABC}$ subtends a right angle at the centre. The area of the minor segment formed by $\widehat{ABC}$ is $14.25\,cm^2$ and the area of $\Delta OAC$ is $25\,cm^2$. Then,the area of the minor sector formed by $\widehat{ABC}$ is $\ldots \ldots \ldots cm^2$.