$A$ cylindrical tank is closed at both the ends by hemispheres. Its radius is $2.1 \,m$ and the total height is $9.2 \,m$. How many litres of petrol can it contain?

$A$ building is in the form of a cylinder surmounted by a hemispherical dome (see figure). The base diameter of the dome is equal to $\frac{2}{3}$ of the total height of the building. Find the height of the building,if it contains $67 \frac{1}{21} \, m^3$ of air. (in $m$)

Six wooden cubes of length $3 \, cm$ are arranged in a row touching each other face to face. Find the total surface area of the solid formed in this manner. (in $cm^2$)

Write 'True' or 'False' and justify your answer:
$A$ solid ball is exactly fitted inside a cubical box of side $a$. The volume of the ball is $\frac{4}{3} \pi a^{3}$.

The base of a cone with radius $0.6 \ m$ and height $1.6 \ m$ is hemispherical. Find the volume of this combined solid in $m^{3}$.

$A$ metallic cylinder with diameter $1 \, cm$ and height $4 \, cm$ is melted and recast to produce balls of radius $\frac{1}{8} \, cm$. Find the number of balls produced.