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

In a circle,the area of a sector formed by two radii perpendicular to each other is $38.5 \, cm^2$. Find the radius of the circle (in $cm$).

Find the area of the shaded region in the figure where arcs drawn with centers $A, B, C,$ and $D$ intersect in pairs at mid-points $P, Q, R,$ and $S$ of the sides $AB, BC, CD,$ and $DA,$ respectively of a square $ABCD$ (Use $\pi = 3.14$) (in $cm^{2}$).

The area of a sector formed by a $12\,cm$ long arc in a circle with radius $12\,cm$ is $\ldots \ldots \ldots \, cm^{2}$.

The side length of square $ABCD$ shown in the diagram is $42 \ cm$. The shaded design is formed by drawing semicircles on all the sides of the square. Find the area of the shaded design in $cm^2$.

Find the area of a sector of a circle of radius $28 \,cm$ and central angle $45^{\circ}$. (in $cm^{2}$)