The length, width and height of a cuboid are in the ratio 10 : 17 : 14, and its total surface area is 1096 cm². Find the length (in cm) of the cuboid.

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Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 09 Jun, 2025 Shift 1)

Answer 1

Given:

The length, width, and height of a cuboid are in the ratio 10:17:14.

Total surface area = 1096 cm²

Formula used:

Total surface area of a cuboid = 2 × (length × width + width × height + height × length)

Let the length = 10x, width = 17x, and height = 14x.

Calculation:

Total surface area = 2 × (length × width + width × height + height × length)

1096 = 2 × [(10x × 17x) + (17x × 14x) + (14x × 10x)]

⇒ 1096 = 2 × [170x² + 238x² + 140x²]

⇒ 1096 = 2 × 548x²

⇒ 1096 = 1096x²

⇒ x² = 1

⇒ x = 1

Length = 10x = 10 × 1 = 10 cm

∴ The correct answer is option (3).

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