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Two square pyramids have equal volumes. The base edge of one is half the base edge of the other. The height of the second pyramid is what multiple of the height of the first?
Answer & Solution
Correct answer: C.
1. Let base edges be a and a/2. Equal volume condition: (1/3)a²h₁ = (1/3)(a/2)² h₂.
2. Simplify: a²h₁ = (a²/4) h₂.
3. So h₂ = 4 h₁, meaning the second pyramid is FOUR times taller, not the inverse.
4. Rephrased: h₂/h₁ = 4 — the smaller-base pyramid needs 4× the height to match volume.
5. Equivalently, h₁ = h₂/4, so the first pyramid's height is 1/4 of the second's — and we asked what fraction the FIRST is of the second.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7-8 (pp 180-199, 2019 ed.)._
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