From a solid cube of side $7 \, cm$,a conical cavity of height $7 \, cm$ and radius $3 \, cm$ is hollowed out. Find the volume of the remaining solid (in $cm^3$).

For a bucket in the shape of a frustum of a cone,the radii are $28\,cm$ and $7\,cm$ and the height is $45\,cm$. How many litres of water can it hold?

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 $cm^3$.

$A$ canal is $300 \,cm$ wide and $120 \,cm$ deep. The water in the canal is flowing with a speed of $20 \,km/h$. How much area will it irrigate in $20 \,minutes$ if $8 \,cm$ of standing water is desired? (in $hectares$)

The ratio of diameters of two cones is $2:3$ and the ratio of their heights is $9:4$. Then,the ratio of their volumes is:

$A$ 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 $cm^3$).