The length,breadth,and height of a cuboidal box are $25 \, cm$,$20 \, cm$,and $10 \, cm$ respectively. Find its total surface area in $cm^2$.

The volume of a cuboid with length $25\, cm$ and breadth $15\, cm$ is equal to the volume of a cube with edge $15\, cm$. Find the height of the cuboid (in $cm$).

The areas of the three adjacent faces meeting at one vertex of a cuboid are $4000 \, cm^2$,$2000 \, cm^2$,and $3200 \, cm^2$ respectively. Find the dimensions and the volume of the cuboid.

Lateral surface area of a cuboid $= \ldots \ldots \ldots$

Find the total surface area of a hemisphere of radius $42 \, cm$. (in $cm^2$)

$A$ cylindrical container of radius $14\, cm$ is partially filled with water. $A$ solid cuboid of iron with dimensions $22\, cm \times 16\, cm \times 7\, cm$ is submerged in it. Find the rise in the level of the water when the solid is completely submerged. (in $cm$)