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 ₹)

The length of a square field is $50 \, m$. $A$ cow is tethered at one of the vertices by a $3 \, m$ long rope. Find the area of the region of the field in which the cow can graze. $(\pi = 3.14)$ (in $m^2$)

While calculating the area of a circle,its radius was taken to be $6 \, cm$ instead of $5 \, cm$. The calculated area is $\dots \%$ more than the actual area.

The maximum area of a triangle inscribed in a semicircle having radius $10 \, cm$ is $\ldots \ldots \ldots \, cm^2$.

In the figure,arcs are drawn by taking vertices $A, B$ and $C$ of an equilateral triangle of side $10 \, cm$ as centers to intersect the sides $BC, CA$ and $AB$ at their respective mid-points $D, E$ and $F$. Find the area of the shaded region (Use $\pi = 3.14$) (in $cm^2$).

$A$ wire fence is to be put up all around a circular ground with diameter $105 \, m$. The length of the fence is $\ldots \ldots \ldots \ldots \, m$.