$A$ 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.

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

Curved surface area of a cone is $308 \, cm^2$ and its slant height is $14 \, cm$. Find $(i)$ radius of the base and $(ii)$ total surface area of the cone.

The length,breadth,and height of a room are $5\, m$,$4\, m$,and $3\, m$ respectively. Find the cost of whitewashing the walls of the room and the ceiling at the rate of $Rs. 7.50$ per $m^2$.

$A$ wooden bookshelf has external dimensions as follows: Height $= 110\, cm$,Depth $= 25\, cm$,Breadth $= 85\, cm$ (see Fig.). The thickness of the plank is $5\, cm$ everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is $20$ paise per $cm^2$ and the rate of painting is $10$ paise per $cm^2$,find the total expenses required for polishing and painting the surface of the bookshelf.

$A$ patient in a hospital is given soup daily in a cylindrical bowl of diameter $7 \, cm$. If the bowl is filled with soup to a height of $4 \, cm$, how much soup does the hospital have to prepare daily to serve $250$ patients?