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 $\pi$)

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?

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

In a circle with radius $11.2 \, cm$,two radii are perpendicular to each other. Find the area of the minor sector,the major sector,and the minor segment corresponding to these radii.

From each corner of a square of side $4\, cm$,a quadrant of a circle of radius $1\, cm$ is cut and also a circle of diameter $2\, cm$ is cut as shown in the figure. Find the area of the remaining portion of the square. [Use $\pi = \frac{22}{7}$]

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 $m$)