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 area of a circle is $200 \, cm^{2}$. Then,the area of a minor sector of that circle can be $\ldots \ldots \ldots \, cm^{2}$.

The length of the minute hand of a clock is $14 \, cm$. If the minute hand moves from $1$ to $10$ on the dial,then $\ldots \ldots \ldots \ldots \, cm^2$ area will be covered.

In $\odot(O, 4 \, cm)$,the length of chord $\overline{AB}$ is $4 \, cm$. Then,$m \angle AOB = \ldots$ (in $^\circ$)

The side length of square $ABCD$ is $14 \, cm$. As shown in the diagram,circles with radius $7 \, cm$ are drawn with each vertex as the centre so that each circle touches two other circles externally. Find the area of the shaded region in $cm^2$.

The maximum area of a triangle inscribed in a semicircle with diameter $50 \, cm$ is ........... $cm^{2}$.