GIVEN: Surface area of a cuboid = 376 cm2 Ratio of length, breadth, and height of the cuboid = 5 : 4 : 3 CONCEPT: Area and volume of 2-D and 3-D shapes. FORMULA USED: Surface area of cuboid = 2(lb + bh + lh) Diagonal of cuboid = √ (l2+b2+h2) Diagonal of cube = a√3 CALCULATION: Let the length, breadth, and height of the cuboid are ‘5x’, ‘4x’, and ‘3x’ respectively. According to the question, 2[(5x × 4x) + (4x × 3x) + (5x × 3x)] = 376 ⇒2[20x2+12x2+15x2]=376 ⇒ x = 2 So, the length, breadth and height of the cuboid are 10 cm, 8 cm, and 6 cm respectively. Now, The main diagonal of the cuboid = √ (102+82+62) = 10√2 cm ⇒ The side of the cube = 10√2 cm ∴ Main diagonal of the cube = 10√2 × √3 = 10√6 cm