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 $Rs.$)

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,$AB$ and $CD$ are two diameters of a circle (with centre $O$) perpendicular to each other. $OD$ is the diameter of the smaller circle. If $OA = 7 \, cm$,find the area of the shaded region in $cm^2$. [Use $\pi = \frac{22}{7}$]

$A$ 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 $\pi = 3.14$)

The figure depicts a racing track whose left and right ends are semicircular.
The distance between the two inner parallel line segments is $60 \, m$ and they are each $106 \, m$ long. If the track is $10 \, m$ wide,find:
$(i)$ the distance around the track along its inner edge
$(ii)$ the area of the track. $\left[ \text{Use } \pi = \frac{22}{7} \right]$

In the given figure,$OACB$ is a quadrant of a circle with centre $O$ and radius $3.5 \, cm$. If $OD = 2 \, cm$,find the area of the:
$(i)$ quadrant $OACB$,
$(ii)$ shaded region. $\left[ \text{Use } \pi = \frac{22}{7} \right]$