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 ........

If the radius of a circle is doubled,its area becomes $\ldots \ldots \ldots$ times the area of the original circle.

In a circle with radius $21 \, cm$,the length of a minor arc is $33 \, cm$. Find the measure of the angle subtended at the centre by this arc. Also,find the area of the minor sector and the area of the minor segment formed by it.

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

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 $m^2$)