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

As shown in the diagram, $\overline{ AC }$ is a diameter of the circle with centre O. $\Delta ABC$ is inscribed in a semicircle of the circle. If $AC =35 \,cm$, $AB =21\, cm$ and $BC =28\, cm ,$ find the area of the shaded region. (in $cm^2$)

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii $24 \,cm$ and $7 \,cm$ is (in $cm$)

In $Fig.$ arcs are drawn by taking vertices $A , B$ and $C$ of an equilateral triangle of side $10 \, cm$. to intersect the sides $BC, CA$ and $AB$ at their respective mid-points $D , E$ and $F$. Find the area of the shaded region (Use $\pi=3.14)$ (in $cm ^{2}$)

Four circular cardboard pieces of radii $7\, cm$ are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces. (in $cm^2$)

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