In a circle with radius $50 \, cm$,the area of the sector formed by a $20 \, cm$ long arc is $\ldots \ldots \ldots cm^2$.

In a circle,the ratio of the areas of two distinct minor sectors is $1:4$. Then,the ratio of the angles at the centre for those minor sectors is $\ldots \ldots \ldots \ldots$.

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 a circle with radius $6.3 \ cm$,an arc subtends an angle of measure $150^{\circ}$ at the centre. Find the length of this arc and the area of the sector formed by this arc.

The maximum area of a triangle inscribed in a semicircle with diameter $50 \, cm$ is ........... $cm^{2}$.

Area of a circle is $5544 \, cm^{2}$. Find its radius (in $cm$).