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 .........
$30$
$60$
$90$
$120$
The area of $\odot( O , r)$ is $240\,cm ^{2} .$ In $\odot( O , r),$ minor $\widehat{ ACB }$ subtends an angle of measure $45$ at the centre. Then, the area of minor sector $OACB$ is $\ldots \ldots \ldots . . cm ^{2}$.
Find the area of the flower bed (with semi-circular ends) shown in $Fig.$
In a circle with radius $10\, cm ,$ the area of a minor sector is $75 \,cm ^{2}$. Then, the length of the arc of that sector is $\ldots \ldots \ldots . . cm$.
Find the diameter of the circle whose area is equal to the sum of the areas of the two circles of diameters $20\, cm$ and $48 \,cm .$ (in $cm$)
It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16\, m$ and $12 \,m$ in a locality. The radius of the new park would be (in $m$)