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Mathematics — CBSE Class 10 board question

Q1. [1]
**Assertion (A):** Two cubes each of edge length 10 cm are joined together. The total surface area of newly formed cuboid is 1200 cm². **Reason (R):** Area of each surface of a cube of side 10 cm is 100 cm².
  1. (A) Both Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A).
  2. (B) Both Assertion (A) and Reason (R) are true. Reason (R) does not give correct explanation of (A).
  3. (C) Assertion (A) is true but Reason (R) is not true.
  4. (D) Assertion (A) is not true but Reason (R) is true.
Previously asked in CBSE board exam
2024 30/2/1 Q20
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer

(D) Assertion (A) is not true but Reason (R) is true.

When two cubes of edge 10 cm are joined, the cuboid formed is 20 cm × 10 cm × 10 cm. TSA = 2(20×10 + 10×10 + 20×10) = 2(200+100+200) = 1000 cm², not 1200 cm². Reason (R) is correct: each face of a 10 cm cube = 10×10 = 100 cm².

Explanation

When two cubes are joined end-to-end, two faces (one from each cube) are hidden, so the total surface area decreases. Original TSA of two cubes = 2 × 600 = 1200 cm², but joining removes 2 faces of 100 cm² each, giving 1200 − 200 = 1000 cm². The Assertion states 1200 cm², which is wrong. Reason (R) is independently correct (area of each face = 100 cm²), so answer is (D).

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