$A$ chord of a circle of radius $12 \, cm$ subtends an angle of $120^{\circ}$ at the centre. Find the area of the corresponding segment of the circle. (in $cm^2$)
(Use $\pi = 3.14$ and $\sqrt{3} = 1.73$)

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

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

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 $cm$)

$A$ round table cover has six equal designs as shown in the figure. If the radius of the cover is $28\, cm$,find the cost of making the designs at the rate of $Rs.\, 0.35$ per $cm^2$. (in $Rs.$) (Use $\sqrt{3}=1.7$)

The cost of fencing a circular field at the rate of $Rs. 24$ per metre is $Rs. 5280$. The field is to be ploughed at the rate of $Rs. 0.50$ per $m^2$. Find the cost of ploughing the field (Take $\pi = \frac{22}{7}$). (in $Rs.$)