The radii of two circles are $8 \, cm$ and $6 \, cm$ respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles. [use $\pi = \frac{22}{7}$] (in $cm$)

$A$ car has two wipers which do not overlap. Each wiper has a blade of length $25 \, cm$ sweeping through an angle of $115^{\circ}.$ Find the total area cleaned at each sweep of the blades. [use $\pi=\frac{22}{7}$]

Find the area of the shaded region in the figure,where $ABCD$ is a square of side $14 \, cm$. (in $cm^2$)

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

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 a circle of radius $21\, cm$,an arc subtends an angle of $60^{\circ}$ at the centre. Find:
$(i)$ the length of the arc
$(ii)$ area of the sector formed by the arc
$(iii)$ area of the segment formed by the corresponding chord [Use $\pi = \frac{22}{7}$]