The length, breadth and height of a cuboidal box are in the ratio 7 : 5 : 3 and its whole surface area is 27832 cm². Its volume is:

288120 cm³

We know that,

Total surface area of cuboid = 2(lb + bh + hl)

Volume of the cuboidal box = lbh

Ratio of length, breadth and height of cuboidal box = 7a : 5a : 3a

Total surface are of cuboidal box = 2 (7a × 5a + 5a × 3a + 3a × 7a) = 27832

= (35a² + 15a² + 21a²) = \(\frac{27832}{2}\)

= 71x² = 13916

= a² = 196

= a = \(\sqrt {196}\)

= a = 14

Volume of the cuboidal box = 7a × 5a × 3a = 105 × 14 × 14 × 14 = 288120