The diameter of a roller is $84\, cm$ and its length is $120\, cm$. It takes $500$ complete revolutions to move once over to level a playground. Find the area of the playground in $m^2$. $\left[\text{Assume } \pi = \frac{22}{7}\right]$ (in $, m^2$)

Find the capacity in litres of a conical vessel with radius $7 \, cm$ and slant height $25 \, cm$. (in $, l$)

$A$ hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is $17.6 \, m$,find the cost of painting it,given the cost of painting is $Rs. 5$ per $100 \, cm^2$.

Find the volume of the right circular cone with radius $6 \, cm$ and height $7 \, cm$. Assume $\pi = \frac{22}{7}$. (in $, cm^3$)

$A$ dome of a building is in the form of a hemisphere. From inside,it was white-washed at the cost of $Rs. 4989.60$. If the cost of white-washing is $Rs. 20$ per square metre,find the inside surface area of the dome. (in $, m^2$)

$A$ right triangle $ABC$ with sides $5 \, cm, 12 \, cm$ and $13 \, cm$ is revolved about the side $12 \, cm$. Find the volume of the solid so obtained. Also,find the volume of the solid obtained when the same triangle is revolved about the side $5 \, cm$. Finally,find the ratio of the volumes of the two solids.