$A$ 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 total surface area of a cone,if its slant height is $21 \, m$ and diameter of its base is $24 \, m$. (Take $\pi = \frac{22}{7}$) (in $, m^2$)

$A$ 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.

$A$ hemispherical tank is made up of an iron sheet $1 \,cm$ thick. If the inner radius is $1 \,m$,then find the volume of the iron used to make the tank. (in $,m^3$)

$A$ hemispherical bowl has a radius of $3.5\, cm$. What would be the volume of water it would contain (in $, cm^{3}$)?

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.