Write 'True' or 'False' and justify your answer:
Two identical solid hemispheres of equal base radius $r \text{ cm}$ are joined together along their bases. The total surface area of the resulting solid is $6 \pi r^{2}$.

The base of a cone is hemispherical. The radius of the cone is $15 \, cm$ and the total height of the solid is $55 \, cm$. Find the volume of this solid (in $cm^3$).

The volume of a cylinder is $550 \, cm^3$ and its radius is $5 \, cm$. Then,its height is ....... $cm$.

Write 'True' or 'False' and justify your answer:
$A$ solid cone of radius $r$ and height $h$ is placed over a solid cylinder having the same base radius and height as that of the cone. The total surface area of the combined solid is $\pi[\sqrt{r^{2}+h^{2}}+3r+2h]$.

$A$ metallic sphere with radius $6 \, cm$ is melted and recast into a wire of radius $0.4 \, cm$. Find the length of the wire in metres.

The slant height of a cone with radius $6 \, cm$ and height $8 \, cm$ is $\ldots \ldots \ldots \ldots cm$.