The diameter of a circular garden is $210 \,m$. Inside it,all along the boundary,there is a path of uniform width $7 \,m$. Then,the area of the path is $\ldots \ldots \ldots \ldots \,m^2$.

The union of a chord of a circle and its corresponding arc is called $\ldots \ldots \ldots \ldots$

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 $cm$)

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.

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 ........

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 $cm^2$)