The radius of a hemispherical bowl is $9 \, cm$. It is completely filled with some medicine. If this medicine is filled in cylindrical bottles of diameter $3 \, cm$ and height $4 \, cm$,how many bottles can be filled?

$A$ 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.

How many balls of radius $1.4 \, cm$ can be produced by melting a metallic sphere of radius $42 \, cm$?

$A$ cone of radius $4 \, cm$ is divided into two parts by drawing a plane through the midpoint of its axis and parallel to its base. Compare the volumes of the two parts.

Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses,which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as $30 \,cm$ and $35 \,cm$ and the vertical height of the mould is $14 \,cm$ (see figure). If each $cm^3$ of molasses has a mass of about $1.2 \,g$,find the mass of the molasses that can be poured into each mould (in $kg$). [Take $\pi = \frac{22}{7}$]

$A$ 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 $m$)