In the figure, a circle of radius $7.5 \, cm$ is inscribed in a square. Find the area of the shaded region (Use $\pi = 3.14$) (in $cm^2$).

In $\odot(O, 7),$ the length of $\widehat{ABC}$ is $14.$ Then,$\ldots \ldots$ holds good.

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii $15 \, cm$ and $18 \, cm$ (in $cm$).

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 ........

The length of the minute hand of a clock is $5\, cm$. Find the area swept by the minute hand during the time period $6:05\, a.m.$ and $6:40\, a.m.$ (in $cm^2$).

The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?