The radius and height of a cone are both $3 \, cm$. Then,its volume is $\ldots \ldots \ldots \, cm^{3}$. (in $\pi$)

The base of a cone with radius $14 \, cm$ and height $32 \, cm$ is hemispherical. Find its volume in $cm^3$.

Total surface area of a hemisphere $= \ldots \ldots \ldots . . .$

Write 'True' or 'False' and justify your answer:
The actual capacity of a vessel as shown in the figure is equal to the difference between the volume of the cylinder and the volume of the hemisphere.

The shape of a lump of jaggery is that of a frustum of a cone. Its radii are $14 \, cm$ and $7 \, cm$ and height is $12 \, cm$. Find the volume of the lump of jaggery (in $cm^3$).

The rainwater from a roof of dimensions $22 \, m \times 20 \, m$ drains into a cylindrical vessel having a base diameter of $2 \, m$ and a height of $3.5 \, m$. If the rainwater collected from the roof just fills the cylindrical vessel,find the rainfall in $cm$.