As shown in the diagram, rectangle $ABCD$ is a metal sheet in which $CD = 20 \, cm$ and $BC = 14 \, cm$. From it, a semicircle with diameter $\overline{BC}$ and a sector with centre $A$ and radius $AD$ is cut off. Find the area of the remaining sheet 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 $cm$)

Two minor sectors of two distinct circles have the measure of the angle at the centre equal. If the ratio of their areas is $4:9,$ then the ratio of the radii of the circles is ........

The union of a chord of a circle and its corresponding arc is called $\ldots \ldots \ldots \ldots$

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 cost of erecting a wall all around a circular ground at the rate of $₹ 60/m$ is $₹ 26,400$. Find the cost of levelling the ground at the rate of $₹ 50/m^2$. (in $₹$) (in $1,000$)