In $\odot(O, r)$,the length of minor $\widehat{ACB}$ is $\frac{1}{6}$ times the circumference of the circle. Then,the measure of the angle subtended at the centre by minor $\widehat{ACB}$ is ......... (in $^{\circ}$)

In $\odot(O, r)$,chord $\overline{AB}$ subtends a right angle at the centre. The area of the minor segment $\overline{AB} \cup \widehat{ACB}$ is $114 \, cm^2$ and the area of $\Delta OAB$ is $200 \, cm^2$. Then,the area of the minor sector $OACB$ is ......... $cm^2$.

If the area of a circle is $154 \, cm^2$,then its perimeter (circumference) is (in $cm$):

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 $m^2$)

In a circle with radius $56 \, cm$,find the area of the minor sector,the major sector,and the minor segment corresponding to two radii perpendicular to each other.

If the length of an arc of a circle of radius $r$ is equal to that of an arc of a circle of radius $2r$,then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false? Why?