Q1. [1]
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).
If a question refers to an image, map, graph or diagram that is not shown here, open the Study Guide single page app, go to
Library and find the actual CBSE question paper. The original papers are also available on the CBSE website:
cbse.gov.in.