$A$ solid metallic hemisphere of radius $8 \, cm$ is melted and recast into a right circular cone of base radius $6 \, cm$. Determine the height of the cone (in $cm$).

$16$ 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 volume of the largest right circular cone that can be cut out from a cube of edge $4.2 \,cm$ is (in $cm^3$)

The volume of a sphere with diameter $10 \, cm$ is $\ldots \ldots \, cm^3$.

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 $\text{cm}$).

Volume of a cone $= \dots$