📑 Table of Contents
Quick Navigation
The Infinite Pyramid Proof
Imagine dissecting a sphere into millions of tiny pyramids whose apexes meet at the sphere's geometric center:
- The height of each pyramid is the radius: = r$.
- Volume of each pyramid: {pyramid} = ⅓ imes ext{Base Area} imes h = ⅓ imes ext{Base Area} imes r$.
- Summing all pyramids: {sphere} = ⅓ imes (\sum ext{Base Areas}) imes r$.
- The sum of all pyramid bases is the sphere's surface area: $4\pi r^2$.
- Substituting gives: = ⅓ imes (4\pi r^2) imes r = ⁴⁄₃\pi r^3$!