The radius of a cone is $15 \, cm$ and its base is hemispherical. If the total height of the solid is $55 \, cm$,find its volume in $cm^3$.

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.

Total surface area of a cylinder with radius $7 \, cm$ and height $13 \, cm$ is $\ldots \ldots \ldots \ldots \, cm^{2}$.

Curved surface area of a cylinder $= \ldots \ldots \ldots \ldots$

The radii of a frustum of a cone are $6 \, cm$ and $4 \, cm$. If its height is $9 \, cm$,its volume is $\ldots \ldots \ldots \pi \, cm^3$.

$A$ 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 $cm$):