How many balls of radius $0.5\, cm$ can be produced by melting a metallic cylinder with radius $4\, cm$ and height $3\, cm$?

Three cubes of a metal whose edges are in the ratio $3:4:5$ are melted and converted into a single cube whose diagonal is $12\sqrt{3} \, \text{cm}$. Find the edges of the three cubes (in $\text{cm}$).

$A$ cone of radius $8 \, cm$ and height $12 \, cm$ is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of the two parts.

The base of a cone is hemispherical. The radius of the cone is $15 \, cm$ and the total height of the solid is $55 \, cm$. Find the volume of this solid (in $cm^3$).

The area of the base of a cone is $60 \, cm^{2}$ and its height is $15 \, cm$. Then,the volume of the cone is $\ldots \ldots \ldots \, cm^{3}$.

The volume of a cone with radius $5 \, cm$ and height $21 \, cm$ is $\ldots \ldots \ldots \, cm^{3}$.