The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?

Find the difference of the areas of two segments of a circle formed by a chord of length $5 \, cm$ subtending an angle of $90^{\circ}$ at the centre.

In $\odot(O, 6)$, $\widehat{ABC}$ is a major arc and $m \angle AOC = 60^{\circ}$. Then, the length of major $\widehat{ABC}$ is ........... (in $\pi$)

The length of a square field is $50 \, m$. $A$ cow is tethered at one of the vertices by a $3 \, m$ long rope. Find the area of the region of the field in which the cow can graze. $(\pi = 3.14)$ (in $m^2$)

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 $\odot(O, r)$,minor $\widehat{ACB}$ subtends an angle of measure $72^{\circ}$ at the centre. Then,the ratio of the length of minor $\widehat{ACB}$ and the circumference of the circle is ............