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 diameters of front and rear wheels of a tractor are $80 \,cm$ and $2 \,m$ respectively. Find the number of revolutions that the rear wheel will make in covering a distance in which the front wheel makes $1400$ revolutions.

The radius of a wheel of a car is $21 \, cm$. If it makes $800$ rotations per minute,find the speed of the car in $km/h$.

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

In a circle with radius $20 \,cm$,the measures of the angle subtended at the centre for two distinct sectors are $15^{\circ}$ and $90^{\circ}$. Then,the ratio of the areas of those sectors is $\ldots \ldots \ldots$.

Is it true to say that the area of a square inscribed in a circle of diameter $p \, cm$ is $p^{2} \, cm^{2}$? Why?