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 $cm^2$)

In the figure,a square is inscribed in a circle of diameter $d$ and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

Find the area of the shaded region in the given figure.

The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters $36 \, cm$ and $20 \, cm$ is (in $cm$)

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 $cm^{2}$).

The area of a minor sector of $\odot(P, 30)$ is $300 \, cm^2$. The length of the arc corresponding to it is .......... $cm$.