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Two cones have equal volumes. Their base radii are in the ratio 4 : 5. The ratio of their heights is:
Answer & Solution
Correct answer: D.
1. Equal volume condition: (1/3) π r₁² h₁ = (1/3) π r₂² h₂.
2. So r₁² h₁ = r₂² h₂, giving h₁ : h₂ = r₂² : r₁².
3. With r₁ : r₂ = 4 : 5, h₁ : h₂ = 5² : 4² = 25 : 16.
4. So heights are in the ratio 25 : 16.
5. Smaller base radius needs more height to match the volume.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._
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