What is the area (in $cm^2$) of a square inscribed in a circle of radius $8 \, cm$?

In a circle with radius $r,$ an arc subtends an angle of measure $\theta$ at the centre. Then,the area of the major sector is $=$ ..........

In $\odot(O, r)$,the length of minor $\widehat{ACB}$ is one-eighth of the circumference of the circle. Then,the measure of the angle subtended at the centre by that arc is $\ldots \ldots \ldots \ldots$ (in $^\circ$)

In the adjoining diagram, $\overline{ AB }$ and $\overline{ CD }$ are diameters of $\odot( O , 7\, cm )$ perpendicular to each other. $A$ circle is drawn with diameter $\overline{ OD }$. Find the area of the shaded region. (in $cm^2$)

The radius of a circular ground is $63 \, m$. Find the cost of fencing its boundary at the rate of ₹ $50 / m$. Find the cost of levelling the ground at the rate of ₹ $40 / m^2$.

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii $24 \, cm$ and $7 \, cm$ is (in $cm$):