The length of a minor arc of a circle is given by the formula $\ldots \ldots \ldots \ldots$

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.

In the given diagram,$\Delta ABC$ is a right-angled triangle in which $m \angle B = 90^{\circ}$ and $AB = BC = 14 \text{ cm}$. $A$ minor sector $BAPC$ is a sector of a circle with center $B$ and radius $BA$. $A$ semicircle arc $\widehat{AQC}$ is drawn on diameter $\overline{AC}$. Find the area of the shaded region in $\text{cm}^2$.

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 ₹)

Find the area of a sector of a circle of radius $21 \, cm$ and central angle $120^{\circ}$. (in $cm^{2}$)

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 $m^2$)