The volume of a cone with radius $5 \, cm$ and height $12 \, cm$ is ........ $\pi \, cm^{3}$.

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

The radii of the top and bottom of a bucket of slant height $45 \, cm$ are $28 \, cm$ and $7 \, cm$,respectively. The curved surface area of the bucket is (in $cm^2$)

The ratio of radii of two cylinders is $3:4$ and the ratio of their heights is $4:5$. Then,the ratio of their volumes is ..........