$A$ cone of radius $4 \, cm$ is divided into two parts by drawing a plane through the midpoint of its axis and parallel to its base. Compare the volumes of the two parts.

The volume of a sphere is equal to $\ldots \ldots \ldots . .$

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter $2 \, cm$ and height $16 \, cm$. The diameter of each sphere is (in $cm$):

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 $\text{cm}$).

$16$ glass spheres,each of radius $2 \,cm$,are packed into a cuboidal box of internal dimensions $16 \,cm \times 8 \,cm \times 8 \,cm$. The box is then filled with water. Find the volume of water filled in the box (in $cm^3$).

The radius of a cone is $15 \, cm$ and its base is hemispherical. If the total height of the solid is $55 \, cm$,find its volume in $cm^3$.