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

What is the area (in $cm^2$) of a square inscribed in a circle of radius $8 \, cm$?

In the figure,$AB$ is a diameter of the circle,$AC = 6 \, cm$ and $BC = 8 \, cm$. Find the area of the shaded region (Use $\pi = 3.14$). (in $cm^2$)

Nine circular designs are made in a square show-piece as shown in the diagram. If the radius of each circle is $21\, cm$,find the area of the region without design. (in $cm^2$)

All the vertices of a rhombus lie on a circle. Find the area of the rhombus,if the area of the circle is $1256 \, cm^{2}$. (Use $\pi = 3.14$). (in $cm^{2}$)

In the figure,a circle is inscribed in a square of side $5 \, cm$ and another circle is circumscribing the square. Is it true to say that the area of the outer circle is two times the area of the inner circle? Give reasons for your answer.