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 $\text{cm}$).

Write 'True' or 'False' and justify your answer:
The actual capacity of a vessel as shown in the figure is equal to the difference between the volume of the cylinder and the volume of the hemisphere.

The volume of a cone with radius $5 \, cm$ and height $12 \, cm$ is ........ $\pi \, cm^{3}$.

The barrel of a fountain pen,cylindrical in shape,is $7 \, cm$ long and $5 \, mm$ in diameter. $A$ full barrel of ink in the pen is used up on writing $3300$ words on an average. How many words can be written in a bottle of ink containing one-fifth of a litre?

The ratio of radii of two cylinders is $3:4$ and the ratio of their heights is $4:5$. Then,the ratio of their volumes is ..........

The volume of a sphere with radius $1.5 \text{ cm}$ is $\ldots \ldots \ldots \text{ cm}^3$.