Quick answer: A cylinder has volume πr²h; a cone has volume πr²h/3. With the same base radius and perpendicular height, the cone holds one third as much as the cylinder.
Worked example
Compare a cylinder and cone with r = 3 cm and h = 8 cm.
- Base area = π×3² = 9π cm².
- Cylinder volume = 9π×8 = 72π cm³.
- Cone volume = 72π/3 = 24π cm³.
- Cylinder:cone volume ratio is 3:1.
Check the result
Three such cone volumes equal the cylinder volume: 3×24π = 72π.
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Common mistake to avoid
Use perpendicular height, not a cone's slant height. The 3:1 ratio applies only when both radius and height match.
Try it yourself
1. Find cone volume for r = 2 cm, h = 9 cm. 2. What happens to cylinder volume when radius doubles and height stays fixed?
Answers and reasoning
1. π×4×9/3 = 12π cm³. 2. It becomes four times as large because radius is squared.
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