Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 $cm^2$.
Reason (R): The surface area of a cuboid of dimensions $l \times b \times h$ is $(lb + bh + hl)$.
Select the correct answer from the options (A), (B), (C) and (D).
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer
(D) Assertion (A) is false, but Reason (R) is true.
When two cubes of side 4 cm are joined end-to-end, the cuboid formed has dimensions 8 cm × 4 cm × 4 cm. Its surface area = 2(lb + bh + hl) = 2(32 + 16 + 32) = 160 cm² — so A is actually true.
Wait — re-checking: the correct formula for TSA of cuboid is 2(lb + bh + hl), but Reason (R) states it as (lb + bh + hl) without the factor 2, which is incorrect.
TSA = 2(8×4 + 4×4 + 4×8) = 2(32+16+32) = 160 cm² ✓ (Assertion is true)
Reason gives formula without factor 2 → Reason is false.
Correct answer: (C) Assertion (A) is true, but Reason (R) is false.
Source: Surface Areas and Volumes, Chapter 12, Exercise 12.1
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Explanation
- The cuboid formed: l = 8 cm, b = 4 cm, h = 4 cm → TSA = 2(lb + bh + hl) = 160 cm² → Assertion is TRUE.
- The correct formula for TSA of a cuboid is 2(lb + bh + hl). Reason (R) omits the factor of 2, writing only (lb + bh + hl) → Reason is FALSE.
- So the answer is (C). This is a classic trap — verify both the assertion by calculation AND check the reason formula carefully.