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Geometry
Mensuration 3D
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RRB NTPC Graduate Tier 1 2025 Shift-1 📅 09 Jun, 2025

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.

A
17
B
10
C
1
D
5
Result Summary
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RRB NTPC Graduate Tier 1
2025 • 09 Jun, 2025 • Shift-1
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.
Correct Answer
10
Variable Definition: Let the exact dimensions of the cuboid be defined algebraically as Length (L) = 10x, Width (W) = 17x, and Height (H) = 14x, where x is a co......
Ref/Book : RRB NTPC Graduate Tier 1 2025
Ref. Subject Geometry
Chapter -
Ref. Topic Mensuration 3D
Pg. No -
💡 Analysis & Explanation
Variable Definition ▼
Let the exact dimensions of the cuboid be defined algebraically as Length (L) = 10x, Width (W) = 17x, and Height (H) = 14x, where x is a common multiplier.
Surface Area Formula Application ▼
The formula for Total Surface Area is 2(LW + WH + HL). Plugging in our defined variables gives: 2(10x*17x + 17x*14x + 14x*10x) = 1096. This simplifies to 2(170x² + 238x² + 140x²) = 1096.
Equation Simplification ▼
Combining the internal terms yields 2(548x²) = 1096. Dividing both sides by 2 leaves 548x² = 548. Thus, x² = 1, which implies x = 1.
Final Dimension Calculation ▼
Since x is 1, the Length is simply 10 * 1 = 10 cm.
Conclusion ▼
The exact length of the cuboid is 10 cm.
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