There are two concentric hexagons. Each side of both the hexagons is parallel. Each side of an internal regular hexagon is $8 \mathrm{cm}$. What is the area of the shaded region, if the distance between corresponding parallel sides is $2\sqrt{3} \mathrm{cm}$?

    

In the adjoining diagram ABCD is a square with side 'a' cm. In the diagram the area of the larger circle with centre 'O' is equal to the sum of the areas of the remaining four circles with equal radii, whose centres are P, Q, R and S. What is the ratio between the side of square and radius of a smaller circle?

The radius of a cone is $\sqrt{2}$ times the height of the cone. A cube of the maximum possible volume is cut from the same cone. The ratio of the volume of the cone to the volume of the cube is:

In the following figure, A B C is an equilateral triangle inscribing a square of maximum possible area. Again in this square, there is an equilateral triangle whose side is the same as that of the square. Further, the smaller equilateral triangle inscribes a square of the maximum possible area. What is the area of the innermost square if each side of the outermost triangle be $0.01 \mathrm{m}$ ?