Marbles of diameter $1.4 \,cm$ are dropped into a cylindrical beaker of diameter $7 \,cm$ containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by $5.6 \,cm$.

The formula for finding the total surface area of a cylinder having cone-shaped lids at both the ends will be $\ldots \ldots \ldots \ldots$

Write 'True' or 'False' and justify your answer:
An open metallic bucket is in the shape of a frustum of a cone,mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder.

$A$ 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 $cm^3$).

The radii of a frustum of a cone are $10 \, cm$ and $7 \, cm$. If its height is $4 \, cm$,its curved surface area is $\dots \dots \dots \pi \, cm^2$.

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 $m^{3}$.