The areas of the three adjacent faces of a cuboid are 32 $$cm^2$$, 24 $$cm^2$$ and 48 $$cm^2$$ . What is the volume of the cuboid?

Let the sides of the cuboid is a, b and c.

As per the question, $$a\times b=32 cm^2$$---------(i)

$$b\times c=24 cm^2$$-------(ii)

$$c\times a=48 cm^2$$--------(iii)

Volume of the cuboid$$ = a\times b \times c $$

Now, multiplying equation (i), (ii) and (iii),

$$\Rightarrow a\times b \times b \times c \times c\times a=32\times 24\times 48$$

$$\Rightarrow a \times b\times c=\sqrt{32\times 24\times 48}$$

$$\Rightarrow V = a \times b\times c=\sqrt{32\times 24\times 48}=\sqrt{16\times 48\times 48}$$

$$\Rightarrow V=4\times 48=192cm^3$$