Area of a sector of a circle of radius $36 \, cm$ is $54 \pi \, cm^{2}$. Find the length of the corresponding arc of the sector (in $cm$). (in $pi$)

With the vertices $A, B$ and $C$ of a triangle $ABC$ as centres,arcs are drawn with radii $5 \, cm$ each as shown in the figure. If $AB = 14 \, cm, BC = 48 \, cm$ and $CA = 50 \, cm$,then find the area of the shaded region. (Use $\pi = 3.14$) (in $cm^2$)

If $\theta$ is the angle (in degrees) of a sector of a circle of radius $r$,then the area of the sector is:

The length of the minute hand of a clock is $10.5 \, cm$. Find the area of the region swept by it between $2.25 \, PM$ and $2.40 \, PM$. (in $cm^2$)

The wheel of a motorcycle has a radius of $35 \, cm$. How many revolutions per minute must the wheel make to maintain a speed of $66 \, km/h$?

Will it be true to say that the perimeter of a square circumscribing a circle of radius $a \, cm$ is $8 a \, cm$? Give reasons for your answer.