The areas of three adjacent faces of a solid cuboid are 192 $$cm^2$$​, 242 $$cm^2$$​ and 24 $$cm^2$$​. What is the volume (in $$cm^3$$​) of the cuboid?

The areas of three adjacent faces of a solid cuboid are 192 ​cm²​​, 242 ​cm²​​ and 24 cm²​​.

Area of the face of cuboid = length × breadth, or length × Height, or breadth × Height

Solution:
Let the sides of the cuboid be a, b, and c.
The areas of the faces can be represented as:
Area 1 = ab = 192 cm²
Area 2 = bc = 242 cm²
Area 3 = ca = 24 cm²
Volume of the cuboid = abc
Multiply the three areas:
(ab) × (bc) ×(ca) = 192 × 242 ×24

(abc)² =192 × 242 ×24
abc  =$$\sqrt{192 × 242 ×24}$$​​
abc = 1056 cm³

The volume of the cuboid is 1056 cm³.