The areas of three consecutive faces of a cuboid are 12 cm², then the volume (in cm³) of the cuboid is

Solution (By Examveda Team)

Let the three sides of the cuboid be $$l$$, b and h
⇒ $$l$$b = bh = h$$l$$ = 12
⇒$$l$$²b²h² = 12 × 12 × 12
⇒$$l$$²b²h² = 1728
⇒ $$l$$bh = $$\sqrt {1728} $$
⇒ $$l$$bh = $$12\sqrt {12} $$
⇒ $$l$$bh = $$24\sqrt 3 {\text{ c}}{{\text{m}}^3}$$