PEAZIT Aha card
Go straight to resources ↓A cone fills one third of the matching cylinder
A cone has one third of a cylinder's volume with the same base and perpendicular height. Calculate that cylinder, then divide by three.
| Relation | Meaning |
|---|---|
| V = πr²h / 3 | Circular base area is πr². |
| r = 3; h = 4 | Use perpendicular height, not slant height. |
| V ≈ 3.14 × 9 × 4 / 3 = 37.68 cm³ | Divide the matching cylinder's volume by three. |
One worked example
- V = πr²h / 3Circular base area is πr².
- r = 3; h = 4Use perpendicular height, not slant height.
- V ≈ 3.14 × 9 × 4 / 3 = 37.68 cm³Divide the matching cylinder's volume by three.
Watch out: Perpendicular height runs from apex to base plane. Slant height cannot replace it.
Goal, prerequisites and card origin
What you will learn: Calculate cone volume from radius and perpendicular height.
What you need first: Circle area and cylinder volume.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
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A cone has one third of a cylinder's volume with the same base and perpendicular height. Calculate that cylinder, then divide by three.