Find the area of a sector of a circle with radius $6 \, cm$ if the angle of the sector is $60^{\circ}$. [use $\pi = \frac{22}{7}$]

In the figure,two circular flower beds are shown on two sides of a square lawn $ABCD$ of side $56 \, m$. If the centre of each circular flower bed is the point of intersection $O$ of the diagonals of the square lawn,find the sum of the areas of the lawn and the flower beds (in $m^2$).

Find the area of the shaded region in the figure if $ABCD$ is a square of side $14 \, cm$ and $APD$ and $BPC$ are semicircles. (in $cm^2$) [Use $\pi = \frac{22}{7}$]

Area of a sector of angle $p$ (in degrees) of a circle with radius $R$ is

$A$ brooch is made with silver wire in the form of a circle with diameter $35 \, mm$. The wire is also used in making $5$ diameters which divide the circle into $10$ equal sectors as shown in the figure. Find:
$(i)$ The total length of the silver wire required.
$(ii)$ The area of each sector of the brooch. [Use $\pi = \frac{22}{7}$]

Find the area of the segment $AYB$ shown in the figure if the radius of the circle is $21 \, cm$ and $\angle AOB = 120^{\circ}$. (Use $\pi = \frac{22}{7}$)