The length, breadth and height of a solid cuboidal box are in the ratio 7 ∶ 5 ∶ 3 and its total surface area is 11502 cm². Its breadth is:

Question

Question

This question was previously asked in

SSC GD Constable Previous Year Paper (Held on: 15th December 2021 Shift 3)

Answer 1

Given:

Length : Breadth : Height = 7 : 5 : 3

Total Surface area of cuboidal box = 11502 cm³

Concept Used:

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

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

Calculation:

2 (7a × 5a + 5a × 3a + 3a ×7a) = 11502

⇒ (35a² + 15a² + 21a²) = 11502 / 2

⇒ 71a²= 5751

⇒ a² = 5751/71

⇒ a = √81

⇒ a = 9

So, the breadth of the cuboidal box is 9 × 5 = 45

Shortcut Trick

Here, Breadth is multiplied by 5, then the answer is divisible by 5; only option 45 is divisible by 5.