If the areas of three adjacent faces of a cuboid are $8\ cm^2, 18\ cm^2$ and $25\ cm^2$. Find the volume of the cuboid.

Given:

The areas of three adjacent faces of a cuboid are $8\ cm^2, 18\ cm^2$ and $25\ cm^2$. 

To do:

We have to find the volume of the cuboid.

Solution:

Let $a, b$ and $c$ be the three adjacent faces of the cuboid.

This implies,

$a = 8\ cm^2, b = 18\ cm^2, c = 25\ cm^2$

Let $l, b$ and $h$ be the dimensions of the cuboid.

Therefore,

$a = lb = 8\ cm^2$

$b = bh = 18\ cm^2$

$c = lh = 25\ cm^2$

Volume $= lbh$

$=\sqrt{l b \times b h \times l h}$

$=\sqrt{a b c}$

$=\sqrt{8 \times 18 \times 25}$

$=\sqrt{3600}$

$=60 \mathrm{~cm}^{3}$

The volume of the cuboid is $60\ cm^3$.