Find the area of a sector of a circle of radius $21 \, cm$ and central angle $120^{\circ}$. (in $cm^{2}$)

Calculate the area of the designed region in the figure,which is common between the two quadrants of circles of radius $8 \, cm$ each. $\left[\text{Use } \pi = \frac{22}{7}\right]$

In a circle,the length of a minor arc is $110 \,cm$ and it subtends an angle of measure $150^{\circ}$ at the centre. Then,the radius of the circle is $\ldots \ldots \ldots \ldots \,cm$.

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 $\pi = \frac{22}{7}$]

In the figure,$ABC$ is a quadrant of a circle of radius $14 \, cm$ and a semicircle is drawn with $BC$ as diameter. Find the area of the shaded region. (in $cm^2$) [Use $\pi = \frac{22}{7}$]

Find the area of the minor segment of a circle of radius $14 \, cm$,when the angle of the corresponding sector is $60^{\circ}$. (in $cm^{2}$)