$\widehat{ ACB }$ is a minor arc of $\odot( O , 8 \,cm ) .$ If $m \angle AOB =45,$ the length of minor $\widehat{ ACB }$ is $\ldots \ldots \ldots . . cm .$
$\pi $
$2\pi $
$4\pi $
$8\pi $
The length of square $ABCD$ shown in the diagram is $42\, cm .$ The shaded design is formed by drawing semicircles on all the sides of the square. Find the area of the shaded design. (in $cm^2$)
The radius of a circular ground is $35 \,m$. Outside it, runs a road of width $3.5\, m$. Find the area of the road. (in $m^2$)
In a circle, the area of a sector formed by two radii perpendicular to each other is $38.5 \,cm ^{2}$. Find the radius of the circle. (in $cm$)
An archery target has three regions formed by three concentric circles as shown in $Fig.$ If the diameters of the concentric circles are in the ratio $1: 2: 3,$ then find the ratio of the areas of three regions.
The ratio of radii of two circles is $2: 3$ and the ratio of the angles at centre of two minor sectors of those circles is $5: 2 .$ Then, the ratio of the areas of those sectors is...........