From a solid cube of side $7 \, cm$,a conical cavity of height $7 \, cm$ and radius $3 \, cm$ is hollowed out. Find the volume of the remaining solid (in $cm^3$).

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 $\text{cm}$).

Write 'True' or 'False' and justify your answer:
The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the figure is $\frac{\pi r^{2}}{3} [3 h-2 r]$.

Curved surface area of a cylinder $= \ldots \ldots \ldots \ldots$

Write 'True' or 'False' and justify your answer:
Two identical solid cubes of side $a$ are joined end to end. Then the total surface area of the resulting cuboid is $12 a^{2}$.

Curved surface area of a cone = ....................