Interactive resource
Sphere: 4πr² Area and (4/3)πr³ Volume
Geometry. Interactive 3D sphere — change the radius to see surface area, volume, and scaling laws.
Overview
Both area and volume depend on radius. Double r and area ×4 while volume ×8 — visible in 3D.
Explanation
Surface area S = 4πr² and volume V = (4/3)πr³.
Scaling the radius by k scales area by k² and volume by k³.
Compare with cylinder and cone formulas.
How to use
- Open the sphere scene.
- Orbit the 3D view.
- Adjust radius r.
- Read surface area and volume.
Scaling question
If r doubles, by what factors do area and volume change?
Knowledge points
FAQ
How does this relate to cylinders and cones?
Compare with the cylinder–cone volume tool for shared πr² structure.
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.