$A$ 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 $\sqrt{3} = 1.73$)

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. $\left[ \text{Use } \pi = \frac{22}{7} \right]$

$A$ 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 area of the segment $AYB$ shown in the figure if the radius of the circle is $21 \, cm$ and $\angle AOB = 120^{\circ}$. (Use $\pi = \frac{22}{7}$)

In the figure,a square $OABC$ is inscribed in a quadrant $OPBQ$. If $OA = 20 \, cm,$ find the area of the shaded region. (in $cm^2$) (Use $\pi = 3.14$)

$A$ chord of a circle of radius $10\, cm$ subtends a right angle at the centre. Find the area of the corresponding:
$(i)$ minor segment $\&$ $(ii)$ major sector. (Use $\pi=3.14$ )