Question

If the areas of three adjacent faces of a cuboid are x, y and z, respectively, the volume of the cuboid is
(a) xyz
(b) 2xyz
(c) $\sqrt{xyz}$
(d) $3\sqrt{xyz}$

Answer 1

(c) $\sqrt{xyz}$
Let the length of the cuboid = l
breadth of the cuboid = b
and height of the cuboid = h
Since, the areas of the three adjacent faces are x, y and z, we have:

$$\begin{gathered} lb=x \\ bh=y \\ lh=z \end{gathered}$$

Therefore,

$$\begin{gathered} lb\times bh\times lh=xyz \\ \Rightarrow l^2{b}^2{h}^2=xyz \\ \Rightarrow lbh=\sqrt{xyz} \end{gathered}$$

Hence, the volume of the cuboid $=lbh=\sqrt{xyz}$.