The total surface area of a hemisphere is $4158 \, cm^2$. Find its diameter in $cm$.

$1 \text{ litre} = \ldots \ldots \ldots \text{ cm}^3$

Write True or False and justify your answer in each of the following:
If the radius of a cylinder is doubled and its curved surface area is not changed,the height must be halved.

$A$ storage tank is in the form of a cube. When it is full of water,the volume of water is $15.625 \, m^3$. If the present depth of water is $1.3 \, m$,find the volume of water already used from the tank (in $m^3$).

The circumference of the base of a cylindrical vessel is $440\, cm$ and its height is $80\, cm$. Find the volume of the cylinder in $m^3$.

It costs $Rs. 2200$ to paint the inner curved surface of a cylindrical vessel $10\, m$ deep. If the cost of painting is at the rate of $Rs. 20$ per $m^2$,find the capacity of the vessel. (in $, kl$)