As shown in the diagram,the side length of square $ABCD$ is $35 \, cm$. Two semicircles are drawn on its sides $\overline{AB}$ and $\overline{CD}$ as diameters. Find the area of the shaded region in $cm^2$.

Is the area of the largest circle that can be drawn inside a rectangle of length $a \, cm$ and breadth $b \, cm$ $(a > b)$ equal to $\pi b^{2} \, cm^{2}$? Why?

As shown in the diagram, rectangle $ABCD$ is a metal sheet in which $CD = 20 \, cm$ and $BC = 14 \, cm$. From it, a semicircle with diameter $\overline{BC}$ and a sector with centre $A$ and radius $AD$ is cut off. Find the area of the remaining sheet in $cm^2$.

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

Is the area of the circle inscribed in a square of side $a \, cm$ equal to $\pi a^2 \, cm^2$? Give reasons for your answer.

Areas of two circles are equal. Is it necessary that their circumferences are equal? Why?