Q1. [2] § 12.4 Summary
Three cubes of side 6 cm each, are joined as shown in Figure 1. Find the total surface area of the resulting cuboid.
Previously asked in CBSE board exam
2022 30/3/1 Q4(b) (OR-2)
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer
When three cubes of side 6 cm are joined end-to-end, the resulting cuboid has:
- Length = 6 × 3 = 18 cm, Breadth = 6 cm, Height = 6 cm
Total Surface Area = 2(lb + bh + hl)
= 2(18×6 + 6×6 + 6×18)
= 2(108 + 36 + 108)
= 2 × 252
= 504 cm²
Source: Surface Areas and Volumes, Chapter 12
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Explanation
- The key step is finding the new dimensions of the cuboid: only the length changes (6×3 = 18 cm); breadth and height remain 6 cm each.
- Apply the standard TSA formula for a cuboid: 2(lb + bh + hl). Examiners award 1 mark for correct dimensions/setup and 1 mark for the correct final answer.
- A common error is adding the TSA of three separate cubes — remember, the joined faces are internal and must not be counted.
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