$A$ hemispherical bowl made of brass has an inner diameter of $10.5 \, cm$. Find the cost of tin-plating it on the inside at the rate of $Rs. 16$ per $100 \, cm^2$.

Find the capacity in litres of a conical vessel with height $12 \,cm$ and slant height $13 \,cm$.

$A$ 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 volume of the air inside the dome. (in $, m^3$)

Twenty-seven solid iron spheres,each of radius $r$ and surface area $S$,are melted to form a single sphere with surface area $S'$. Find the ratio of $S$ to $S'$.

Find the surface area of a sphere of radius $7 \, cm$. (in $, cm^{2}$)

The pillars of a temple are cylindrically shaped (see Fig.). If each pillar has a circular base of radius $20\, cm$ and height $10\, m$,how much concrete mixture would be required to build $14$ such pillars (in $, m^3$)?