Q1. [1] § 12.2 Surface Area of a Combination of Solids § 12.3 Volume of a Combination of Solids § 12.4 Summary
If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of cone hollowed out is
- A 1 : 1
- B 1 : 3
- C 2 : 1
- D 3 : 1
Previously asked in CBSE board exam
2025 30/6/1 Q14
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer
Option C: 2 : 1
The cone of greatest volume inside a cylinder has the same base radius and height as the cylinder.
Volume of cylinder = πr²h; Volume of cone = ⅓πr²h.
Remaining wood = πr²h − ⅓πr²h = ⅔πr²h.
Ratio = ⅔πr²h : ⅓πr²h = 2 : 1.
Explanation
The key is recognising that the largest cone carved from a cylinder shares the same radius (r) and height (h). The remaining wood is cylinder minus cone. Examiners expect the ratio simplified to lowest terms: 2:1. Don't confuse this with the cone-to-cylinder ratio (1:3).
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