The length of square $ABCD$ is $14\, cm$. As shown in the diagram, circles with radius $7 \,cm$ are drawn with each vertex as centre so that each circle touches two other circles externally. Find the area of the shaded region. (in $cm^2$)
$42$
$54$
$48$
$54$
The radius of a semicircular garden is $35\,m$. One has to walk $\ldots \ldots \ldots \ldots m$ to make one complete round of that garden.
In $\odot( O , r),$ chord $\overline{ AB }$ subtends a right angle at the centre. The area of minor segment $\overline{ AB } \cup \widehat{ ACB }$ is $114\,cm ^{2}$ and the area of $\Delta OAB$ is $200\,cm ^{2} .$ Then, the area of minor sector $OACB$ is ......... $cm ^{2}$.
The circumference of a circle is $176\,cm$. Then, its radius is $\ldots \ldots \ldots \ldots cm$.
In a circle with centre $O, \overline{O A}$ and $\overline{O B}$ are radii perpendicular to each other. The perimeter of the sector formed by these radii is $75\, cm$. Find the area of the corresponding minor segment. (in $cm^2$)
In a circle, the length of a minor arc is $110 \,cm$ and it subtends an angle of measure $150$ at the centre. Then, the radius of the circle is $\ldots \ldots \ldots \ldots cm$.