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 $1,000$)

The ratio of the areas of the circles with radii $8 \, cm$ and $12 \, cm$ is $\ldots \ldots \ldots \ldots .$

As shown in the diagram,$\overline{AC}$ is a diameter of the circle with centre $O$. $\Delta ABC$ is inscribed in the circle. If $AC = 35 \, cm$,$AB = 21 \, cm$ and $BC = 28 \, cm$,find the area of the shaded region in $cm^2$.

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 $cm^2$.

Is the area of the circle inscribed in a square of side $a \, cm$ equal to $\pi a^2 \, cm^2$? Give reasons for your answer.

Area of a circle is $5544 \, cm^{2}$. Find its radius (in $cm$).