The length of the minute hand of a clock is $17.5\, cm$. Find the area of the region swept by it in $15$ minutes time duration. (in $cm^2$)

The diameter of a circle with area $154\,cm^{2}$ is $\ldots \ldots \ldots . cm$.

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 $cm^{2}$).

With respect to the given diagram,which of the following correctly matches the information in Part $I$ and Part $II$?

Part $I$	Part $II$
$1. \overline{OA} \cup \overline{OB} \cup \widehat{APB}$	$a. \text{Major sector}$
$2. \overline{AB} \cup \widehat{AQB}$	$b. \text{Minor segment}$
$3. \overline{AB} \cup \widehat{APB}$	$c. \text{Minor sector}$
$4. \overline{OA} \cup \overline{OB} \cup \widehat{AQB}$	$d. \text{Major segment}$

An archery target has three regions formed by three concentric circles as shown in the figure. If the diameters of the concentric circles are in the ratio $1: 2: 3$,then find the ratio of the areas of the three regions.

The length of a diagonal of a square inscribed in a circle with radius $10\, cm$ is $\ldots \ldots \ldots . cm$.