Will it be true to say that the perimeter of a square circumscribing a circle of radius $a \,cm$ is $8 a \, cm ?$ Give reasons for your answer.
True Given, radius of circle, $r=a \,cm$
$\therefore$ Diameter of circle, $d=2 \times$ Radius $=2 a\, cm$
$\therefore \quad$ Side of a square $=$ Diameter of circle
$=2 a \,cm$
$\therefore$ Perimeter of a square $=4 \times( Side )=4 \times 2 a$
$=8 a\,cm$
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 ratio of the radii of the circles is ........
In a circle with radius $7\,cm ,$ the perimeter of a minor sector is $\frac{86}{3}\,cm .$ Then, the area of that minor sector is $\ldots \ldots \ldots \ldots cm ^{2}$.
In $\odot( O , r),$ the length of minor $\widehat{ ACB }$ is $\frac{1}{6}$ times the circumference of the circle. Then, the measure of the angle subtended at the centre by minor $\widehat{ ACB }$ is .........
In $\odot( O , 12)$, minor $\widehat{ ACB }$ subtends an angle of measure $30$ at the centre. Then. the length of major $\widehat{A D B}$ is $\ldots \ldots \ldots . . cm .$
In $Fig.$ arcs have been drawn with radii $14\, cm$ each and with centres $P , Q$ and $R$. Find the area of the shaded region. (in $cm ^{2}$)