The volume of a hemisphere with diameter $1 \, cm$ is $\ldots \ldots \, cm^3$.

The diameter of a cylinder is $14\, cm$ and its height is $10\, cm$. Then,the volume of the cylinder is $\ldots \ldots \ldots \ldots cm^3$.

$16$ 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 $cm^3$).

$A$ metallic sphere with radius $42\, cm$ is melted to cast $8000$ identical balls. Find the radius of these balls (in $cm$).

Write 'True' or 'False' and justify your answer:
If a solid cone of base radius $r$ and height $h$ is placed over a solid cylinder having the same base radius and height as that of the cone,then the curved surface area of the shape is $\pi r \sqrt{h^{2} + r^{2}} + 2 \pi r h$.

The radius of a cone is $15 \, cm$ and its base is hemispherical. If the total height of the solid is $55 \, cm$,find its volume in $cm^3$.