$A$ village,having a population of $4000$,requires $150$ litres of water per head per day. It has a tank measuring $20 \,m \times 15 \,m \times 6 \,m$. For how many days will the water of this tank last?

Find the volume of a sphere whose radius is $7 \, cm$. Assume $\pi = \frac{22}{7}$.

The slant height and base diameter of a conical tomb are $25 \, m$ and $14 \, m$ respectively. Find the cost of white-washing its curved surface at the rate of $Rs. 210$ per $100 \, m^2$.

$A$ 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.

The volume of a right circular cone is $9856 \, cm^3$. If the diameter of the base is $28 \, cm$,find the slant height of the cone. (in $, cm$)

$A$ metal pipe is $77\, cm$ long. The inner diameter of a cross section is $4\, cm$,and the outer diameter is $4.4\, cm$. Find its inner curved surface area. (in $, cm^{2}$)