If the areas of three adjacent faces of a cuboidal box are 729 cm², 529 cm² and 289 cm² , respectively, then find the volume of the box.

10557 cm³

We know that,

Area of single cuboidal face = l × b,

Volume of Cuboid = l × b × h 

We have,

Areas of 3 adjacent faces = 729 cm², 529 cm², and 289 cm² 

According to the question, 

 l × b = 729

b × h = 529

h × l = 289

l × b × b × h × h × l = 729 × 529 × 289 

l² × b² × h² = 729 × 529 × 289 

l × b × h = \(\sqrt {729×529×289}\)

= l × b × h = 10557