If the areas of three adjacent faces of a cuboid are x, y and z, respectively, the volume of the cuboid is
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) $\sqrt{x y z}$
(d) $3 \sqrt{x y z}$
Solution:
(c) $\sqrt{x y z}$
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:
$l b=x$
$b h=y$
$l h=z$
Therefore,
$l b \times b h \times l h=x y z$
$\Rightarrow l^{2} b^{2} h^{2}=x y z$
$\Rightarrow l b h=\sqrt{x y z}$
Hence, the volume of the cuboid $=l b h=\sqrt{x y z}$.
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