Find $(i)$ the curved surface area and $(ii)$ the total surface area of a hemisphere of radius $21\, cm$.

$A$ 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 inside surface area of the dome. (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.

The curved surface area of a right circular cylinder of height $14\, cm$ is $88\, cm^2$. Find the diameter of the base of the cylinder.
Assume $\pi = \frac{22}{7}$ unless stated otherwise. (in $, cm$)

In the figure,you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of $20 \, cm$ and a height of $30 \, cm$. $A$ margin of $2.5 \, cm$ is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade. $\left[ \text{Assume } \pi = \frac{22}{7} \right]$ (in $, cm^2$)

The capacity of a closed cylindrical vessel of height $1 \, m$ is $15.4$ litres. How many square metres of metal sheet would be needed to make it (in $, m^{2}$)?