Two minor sectors of two distinct circles have the measure of the angle at the centre equal. If the ratio of their areas is $4:9,$ then the ratio of the radii of the circles is ........

In the figure,a square is inscribed in a circle of diameter $d$ and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

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

The area of the circle that can be inscribed in a square of side $6 \, cm$ is (in $cm^2$) (in $\pi$)

$A$ wire fence is to be put up all around a circular ground with diameter $105 \, m$. The length of the fence is $\ldots \ldots \ldots \ldots \, m$.

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.