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 $cm^2$.

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 ₹)

The area of the circle that can be inscribed in a square of side $6 \, cm$ is (in $cm^2$) (in $\pi$)

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 $=$ ..........

It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16 \, m$ and $12 \, m$ in a locality. The radius of the new park would be (in $m$)

The perimeter of a semicircular table-top is $3.60 \, m$. Then,its radius is $\ldots \ldots \ldots \, cm$.