If the sum of the circumferences of two circles with radii $R_{1}$ and $R_{2}$ is equal to the circumference of a circle of radius $R$,then

On a square cardboard sheet of area $784 \, cm^{2}$, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates (in $cm^{2}$).

In $\odot(O, 6)$, $\widehat{ABC}$ is a major arc and $m \angle AOC = 60^{\circ}$. Then, the length of major $\widehat{ABC}$ is ........... (in $\pi$)

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii $15 \, cm$ and $18 \, cm$ (in $cm$).

In the figure,$AB$ is a diameter of the circle,$AC = 6 \, cm$ and $BC = 8 \, cm$. Find the area of the shaded region (Use $\pi = 3.14$). (in $cm^2$)

In a circle with radius $20\, cm$,the area of a sector formed by an arc of length $10\, cm$ is ............. $cm^2$.