Interactive resource
Cylinder πr²h vs Cone (1/3)πr²h
Geometry. 3D comparison: with the same base and height, a cone is one-third of a cylinder. Free interactive GeoGebra resource — adjust parameters in the…
Overview
Cylinder volume is base × height; cones add the factor 1/3. Three equal cones fill one cylinder.
Explanation
Cylinder volume = base area × height = πr²h.
Cone volume = (1/3)×base×height = (1/3)πr²h.
Three cones fill one cylinder when they share the same base and height.
How to use
- Toggle cylinder vs cone.
- Adjust radius and height.
- Compare volume readouts.
- Remember the 1/3 relationship.
Check the factor
Fix r and h, toggle shapes — is the cylinder about three times the cone?
Knowledge points
FAQ
Must students know the derivation?
Build the 1/3 intuition first; derive or experiment later.
Is this tool free?
Yes. It runs in the browser with no install.
Good for class demos?
Yes — project it and ask what changes when you drag a parameter.
How do I write the formula afterward?
Open the equation editor or symbol sheet and copy a clean expression.