Metallic spheres of radii $6 \, cm$,$8 \, cm$,and $10 \, cm$,respectively,are melted to form a single solid sphere. Find the radius of the resulting sphere (in $cm$).

$A$ bucket is in the form of a frustum of a cone and holds $28.490 \, \text{litres}$ of water. The radii of the top and bottom are $28 \, \text{cm}$ and $21 \, \text{cm}$, respectively. Find the height of the bucket. (in $\text{cm}$)

$500$ persons are taking a dip into a cuboidal pond which is $80 \, m$ long and $50 \, m$ broad. What is the rise of water level in the pond,if the average displacement of the water by a person is $0.04 \, m^3$? (in $cm$)

During the conversion of a solid from one shape to another,the volume of the new shape will

Write 'True' or 'False' and justify your answer:
$A$ spherical steel ball is melted to make eight new identical balls. Then,the radius of each new ball is $\frac{1}{8}$th the radius of the original ball.

The radii of a frustum of a cone are $6 \, cm$ and $4 \, cm$. If its height is $9 \, cm$,its volume is $\ldots \ldots \ldots \pi \, cm^3$.