$3$ solid cubes whose edges are $6, 8$ and $10 \, cm$ respectively,are melted and formed into a single cube. If there is no loss of metal in the process,find the edge of the new cube (in $cm$).

$A$ right prism has a triangular base whose sides are $13\, cm, 20\, cm$ and $21\, cm$. If the altitude of the prism is $9\, cm$,then its volume is......$cm^3$

The volume of the largest right circular cone that can be cut out of a cube of edge $7 \, cm$ is.....$cm^3$

$A$ cylindrical jar of diameter $24\, cm$ contains water to a height of $30\, cm$. $A$ spherical steel ball is dropped into the jar and the level of the water rises by $67.5\, mm$. The diameter of the ball is......$cm$.

$3$ cubes of metal whose edges are in the ratio $3: 4: 5$ are melted into a single cube,the length of whose diagonal is $48 \sqrt{3} \text{ m}$. Calculate the edges of the three cubes.

The volume of a solid cylinder whose base diameter is $14\, mm$ and length is $25\, mm$ is $3850\, mm^3$. If the length of the cylinder is doubled but the diameter is halved,what will be the volume of the resulting cylinder? (in $mm^3$)