In a circle with radius $20 \,cm$, the measures of the angle subtended at the centre for two distinct sectors are $15$ and $90 .$ Then, the ratio of the areas of those sectors is $\ldots \ldots \ldots .$
$1: 4$
$1: 16$
$1: 6$
$1:36$
The length of a square field is $50\, m .$ A cow is tethered at one of the vertices by a $3\, m$ long rope. Find the area of the region of the field in which the cow can graze. $(\pi=3.14)$ (in $m^2$)
Area of a sector of a circle of radius $36\, cm$ is $54 \pi \,cm ^{2}$. Find the length of the corresponding arc of the sector. (in $cm$)
The radius of a circular ground is $63\, m$. Find the cost of fencing its boundary at the rate of ₹ $50 / m .$ Find the cost of levelling the ground at the rate of ₹ $40 / m ^{2}$.
In a circle with radius $6\, cm ,$ a minor are subtends an angle of measure $60$ at the centre. Find the area of the minor sector and the major sector corresponding to that arc.
In a circle with radius $42\, cm ,$ an arc subtends an angle of measure $120$ at the centre. Find the length of this arc and the area of the sector formed by this arc.