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

$A$ horse is tied to a peg at one corner of a square-shaped grass field of side $15 \, m$ by means of a $5 \, m$ long rope (see figure). Find:
$(i)$ The area of that part of the field in which the horse can graze.
$(ii)$ The increase in the grazing area if the rope were $10 \, m$ long instead of $5 \, m$. (Use $\pi = 3.14$)

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii $15 \, cm$ and $18 \, cm$ (in $cm$).

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

The radius of a circular ground is $56\,m$. $A$ $7\,m$ wide road runs around its boundary inside the ground. Some region of the road as shown by the shaded part in the diagram is to be repaired. Find the cost of repairing at the rate of ₹ $40/m^2$ (in ₹).

The radius of a circular ground is $35 \, m$. Inside it,a $3.5 \, m$ broad road runs around its boundary. $A$ part of the road between two radii forming an angle of measure $72^{\circ}$ at the centre is to be repaired. Find the cost of repairing at the rate of ₹ $80 / m^{2}$. (in ₹)