In a circle with radius $6.3 \ cm$,an arc subtends an angle of measure $150^{\circ}$ at the centre. Find the length of this arc and the area of the sector formed by this arc.

The area of an equilateral triangle $ABC$ is $17320.5 \, cm^2$. With each vertex of the triangle as a centre,a circle is drawn with a radius equal to half the length of the side of the triangle (see figure). Find the area of the shaded region in $cm^2$. (Use $\pi = 3.14$ and $\sqrt{3} = 1.73205$)

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

An umbrella has $8$ ribs which are equally spaced. Assuming the umbrella to be a flat circle with radius $56 \, cm$,the area between two consecutive ribs is $\ldots \ldots \ldots \, cm^{2}$.

The length of minor $\widehat{AB}$ of a circle is $\frac{1}{4}$th of its circumference,then the measure of the angle subtended by minor $\widehat{AB}$ at the centre will be $\ldots .$ (in $^{\circ}$)

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.