Introduction / Context:
This tests the known volume relationship between a cylinder and a cone with identical radius and height. It is a standard ratio result used often in mensuration.
Given Data / Assumptions:
- Same radius r and height h for both solids.
- V_cylinder = π r^2 h; V_cone = (1/3) π r^2 h.
Concept / Approach:
- Compare the formulas to find how many cones equal one cylinder.
Step-by-Step Solution:
V_cylinder / V_cone = (π r^2 h) / ((1/3) π r^2 h) = 3.Therefore, 3 cones of the same r and h equal the cylinder volume.
Verification / Alternative check:
Pick any r,h (e.g., r=1, h=1): V_cyl=π; V_cone=π/3; three cones give π.
Why Other Options Are Wrong:
- 2/4/5: Do not match the derived exact ratio of 3.
Common Pitfalls:
- Using 1/2 instead of 1/3 for the cone volume.
- Forgetting the factor 1/3 attached to the cone formula.
Final Answer:
3
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