The length of the minute hand of a clock is $14 \, cm$. Find the area of the region swept by it between $10.10 \, AM$ to $10.30 \, AM$.

The floor of a room has dimensions $5 \, m \times 4 \, m$ and it is covered with circular tiles of diameter $50 \, cm$ each,as shown in the figure. Find the area of the floor that remains uncovered by the tiles. (Use $\pi = 3.14$) (in $m^2$)

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 central angles of two sectors of circles of radii $7 \, cm$ and $21 \, cm$ are respectively $120^{\circ}$ and $40^{\circ}$. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you observe?

Find the difference of the areas of a sector of angle $120^{\circ}$ and its corresponding major sector of a circle of radius $21 \, cm$. (in $cm^2$)

Two minor sectors of two distinct circles have the measure of the angle at the centre equal. If the ratio of their areas is $4:9,$ then the ratio of the radii of the circles is ........