Water is flowing at the rate of $15\, km/h$ through a pipe of diameter $14\, cm$ into a cuboidal pond which is $50\, m$ long and $44\, m$ wide. In what time will the level of water in the pond rise by $21\, cm$? (in $h$)

Three cubes of a metal whose edges are in the ratio $3:4:5$ are melted and converted into a single cube whose diagonal is $12\sqrt{3} \, \text{cm}$. Find the edges of the three cubes (in $\text{cm}$).

Write 'True' or 'False' and justify your answer:
If a solid cone of base radius $r$ and height $h$ is placed over a solid cylinder having the same base radius and height as that of the cone,then the curved surface area of the shape is $\pi r \sqrt{h^{2} + r^{2}} + 2 \pi r h$.

$A$ metallic spherical shell of internal and external diameters $4 \, cm$ and $8 \, cm$,respectively,is melted and recast into the form of a cone of base diameter $8 \, cm$. The height of the cone is (in $cm$):

$A$ top is made by joining a hemisphere to the base of a cone. The radius and the height of the conical part are $2.8 \, cm$ and $6.4 \, cm$ respectively. Find the volume of the top in $cm^3$.

The diameters of a frustum of a cone are $32 \,cm$ and $20 \,cm$. If its height is $8 \,cm$,find its curved surface area and volume. $(\pi = 3.14)$