Three spherical balls of radius $2 \, cm$,$4 \, cm$,and $6 \, cm$ are melted to form a new spherical ball. In this process,there is a loss of $25 \%$ of the material. What is the radius (in $cm$) of the new ball?

$A$ cubical metallic tank whose each edge measures $30\, cm$ is completely filled with water. If $2.7\, litres$ of water is taken out of it, what will be the depth of the remaining water in the tank? (in $cm$)

Surface area of a cube is $600\, cm^{2}$. Find out the length of its diagonal.

Assume that a drop of water is spherical and its diameter is $\frac{1}{10} \text{ cm}$. $A$ conical glass has a height equal to the diameter of its rim. If $32,000$ drops of water fill the glass completely,then the height of the glass (in $\text{cm}$) is:

The height of a cone is $30 \, cm$. $A$ small cone is cut off at the top by a plane parallel to the base. If its volume is $\frac{1}{27}$ of the volume of the given cone,at what height above the base is the section made? (in $cm$)

If the side of a cube is increased by $100 \%$,its volume is increased by (in $\%$)