$A$ cone of radius $8 \, cm$ and height $12 \, cm$ is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of the two parts.

Write 'True' or 'False' and justify your answer:
$A$ solid cylinder of radius $r$ and height $h$ is placed over another cylinder of the same height and radius. The total surface area of the shape so formed is $4 \pi r h + 4 \pi r^2$.

Which of the following gives correctly the capacity of a cubical tank with length $2 \,m$, breadth $2 \,m$, and height $2 \,m$?

$A$ building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains $41 \frac{19}{21} \, m^3$ of air. If the internal diameter of the dome is equal to its total height above the floor,find the height of the building? (in $m$)

$A$ cylinder is closed at both the ends by $30 \, cm$ high cones. The radius of the cylinder is $21 \, cm$ and the total height of the solid is $140 \, cm$. Find the volume of this solid (in $cm^3$).

$CSA$ of a conical tank with height $3\,m$ and diameter $8\,m$ is $\ldots \ldots \ldots \ldots m^{2}$. $(\pi = 3.14)$