The radius of a field in the shape of a sector is $50 \, m$. The cost of fencing its boundary is ₹ $5400$ at the rate of ₹ $30 / m$. Find the cost of tilling at the rate of ₹ $15 / m^2$. (in ₹)

In the given diagram,the shaded portion represents a flower bed in a plot. If $m \angle O = 90^\circ$,$OB = 21 \, \text{m}$,and $OD = 14 \, \text{m}$,find the area of the flower bed in $\text{m}^2$.

If the sum of the areas of two circles with radii $R_{1}$ and $R_{2}$ is equal to the area of a circle of radius $R$,then

As shown in the adjoining diagram,the length of the side of the square plot $ABCD$ is $50 \, m$. At each vertex of the plot,a flower bed in the shape of a sector with radius $10 \, m$ is prepared. Find the area of the plot excluding the flower beds. $(\pi = 3.14)$ (in $m^2$)

Find the area of the shaded region in the figure where arcs drawn with centers $A, B, C,$ and $D$ intersect in pairs at mid-points $P, Q, R,$ and $S$ of the sides $AB, BC, CD,$ and $DA,$ respectively of a square $ABCD$ (Use $\pi = 3.14$) (in $cm^{2}$).

Area of a sector of central angle $200^{\circ}$ of a circle is $770 \, cm^{2}$. Find the length of the corresponding arc of this sector. (in $cm$)