The radii of a bucket in the shape of a frustum of a cone are $28 \, cm$ and $21 \, cm$. If its capacity is $28.490 \, \text{litres}$, find its height in $cm$.

$A$ solid piece of iron in the form of a cuboid of dimensions $49 \, cm \times 33 \, cm \times 24 \, cm$ is moulded to form a solid sphere. The radius of the sphere is (in $cm$):

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 volume of a cone is equal to:

The diameter of a cylinder is $14\, cm$ and its height is $10\, cm$. Then,the volume of the cylinder is $\ldots \ldots \ldots \ldots cm^3$.

How many balls of radius $0.5\, cm$ can be produced by melting a metallic cylinder with radius $4\, cm$ and height $3\, cm$?