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 $cm$).

The length of a minor arc in a circle with radius $28 \ cm$ is $22 \ cm$. Find the measure of the angle subtended at the centre by this arc. Also,find the area of the sector formed by this arc.

The radii of two circles are $8 \, cm$ and $6 \, cm$ respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles. [use $\pi = \frac{22}{7}$] (in $cm$)

In a circle with radius $8.4 \, cm$,two radii are perpendicular to each other. The area of the minor sector formed by these radii is $\ldots \ldots \ldots \, cm^2$.

Is it true to say that the area of a segment of a circle is less than the area of its corresponding sector? Why?

In a circle with radius $14 \, cm$,the area of the minor sector corresponding to minor $\widehat{ACB}$ is $77 \, cm^2$. Then,minor $\widehat{ACB}$ subtends an angle of measure $\dots$ at the centre. (in $^\circ$)