Three metallic solid cubes whose edges are $3 \, cm$,$4 \, cm$,and $5 \, cm$ are melted and formed into a single cube. Find the edge of the cube so formed (in $cm$).

Write 'True' or 'False' and justify your answer:
Total surface area of a lattu (top) as shown in the $Fig.$ is the sum of total surface area of hemisphere and the total surface area of cone.

The radius and the height of a cylinder are $28 \, cm$ and $54.5 \, cm$ respectively. It is closed at one end by a hemisphere and at the other end by a $21 \, cm$ high cone. Find the total surface area of the combined article. (in $cm^2$)

The earth dug out by digging a well with diameter $5.4 \, m$ and depth $20 \, m$ is uniformly spread on a circular ground with radius $15 \, m$. Find the increase in the level of the ground in $cm$.

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

Curved surface area of a hemisphere $= \ldots \ldots \ldots . .$