Find the area of the sector of a circle of radius $5\, cm$,if the corresponding arc length is $3.5\, cm$. (in $cm^2$)

The perimeter of a semicircular table-top is $3.60 \, m$. Then,its radius is $\ldots \ldots \ldots \, cm$.

$A$ calf is tied with a rope of length $6 \,m$ at the corner of a square grassy lawn of side $20 \,m$. If the length of the rope is increased by $5.5 \,m$,find the increase in area of the grassy lawn in which the calf can graze. (in $m^2$)

The area of a square inscribed in a circle with radius $70 \, cm$ is $\ldots \ldots \ldots \, cm^2$.

The central angles of two sectors of circles of radii $7 \, cm$ and $21 \, cm$ are respectively $120^{\circ}$ and $40^{\circ}$. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you observe?

The ratio of the radii of two circles is $4: 5$. Then,the ratio of their areas is...........