Multiple choice general knowledge math & puzzles

What is the volume of cuboid? (A) The lateral surface area of each face is 4,6,9. (B) Sum of the three dimensions (l,b,h) is 10 and the total surface area is 38

  1. The question can be answered by only one of the statements and not by the other statement

  2. The question can be answered by both statements individually

  3. The question can be answered by both statements together

  4. The question cannot be answered.
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A Correct answer
Explanation

Statement A: lh = 4, bh = 6, lb = 9. Volume = lbh. From these: (lh)(bh)(lb) = l²b²h² = 4×6×9 = 216, so lbh = 6. Statement A alone is sufficient. Statement B: l + b + h = 10 and 2(lb + bh + lh) = 38. This gives lb + bh + lh = 19. With l+b+h=10 and sum of pairwise products=19, we can find (l+b+h)² = l²+b²+h²+2(lb+bh+lh), giving sum of squares = 100-38 = 62. But we cannot uniquely determine l, b, h from sum and sum of squares alone. Statement A alone suffices.

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