In a circle with radius $20\, cm ,$ the area of a sector formed by $10\, cm$ long arc is............. $cm ^{2}$
$100$
$200$
$50$
$150$
The length of the minute hand of a clock is $14\, cm .$ The area of the region swept by it in $10$ minutes is $\ldots \ldots \ldots cm ^{2}$.
In a circle with radius $42\,cm ,$ an arc subtends an angle of measure $120$ at the centre. Then, the area of the minor sector formed by that arc is $\ldots \ldots \ldots . . cm ^{2}$.
As shown in the diagram, $\overline{ OA }$ and $\overline{ OB }$ are two radii of $\odot( O , 21 cm )$ perpendicular to each other. If $OD =10 \,cm ,$ find the area of the shaded region. (in $cm^2$)
The length of the minute hand of a clock is $17.5\, cm$. Find the area of the region swept by it in $15$ minutes time duration. (in $cm^2$)
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 ........