Question

The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that
`V^2` = `xyz`

Answer 1

Let a, b, d be the length, breath and height of cuboid then,

`x=ab`
`y=bd`
`z=da, and`
`v=abd`                          `[v=lxxbxxh]`

`⇒xyz=abxxbcxxca= (abc^2)`

`and v= abc`

`v^2=(abc)^2`

`v^2=xyz`