The sides of a cuboid are in the ratio 3 : 4 : 5 and its surface area is equal to the surface area of the cube with side 6 units. What is the approximate volume of the cuboid?

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SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 01 Jul, 2024 Shift 2)

Answer 1

Given:

The sides of the cuboid are in the ratio 3 : 4 : 5.

Surface area of the cube with side 6 units = 6 × 6² = 216 sq units.

Formula Used:

Surface area of cuboid = 2(lw + lh + wh)

Volume of cuboid = l × w × h

Calculation:

Let the sides of the cuboid be 3x, 4x, and 5x.

Surface area of cuboid = 2(3x × 4x + 4x × 5x + 5x × 3x)

Given: Surface area of cuboid = Surface area of cube = 216

⇒ 2(12x² + 20x² + 15x²) = 216

⇒ 2(47x²) = 216

⇒ 94x² = 216

⇒ x² = 216 / 94

⇒ x² ≈ 2.2979

⇒ x ≈ √2.2979

⇒ x ≈ 1.5159

Length = 3x ≈ 3 × 1.5159 ≈ 4.5477

Width = 4x ≈ 4 × 1.5159 ≈ 6.0636

Height = 5x ≈ 5 × 1.5159 ≈ 7.5795

Volume of cuboid = Length × Width × Height

⇒ Volume ≈ 4.5477 × 6.0636 × 7.5795

⇒ Volume ≈ 210

The approximate volume of the cuboid is 210 cubic units.