Math Playground
Geometry

Sphere

Every point the same distance from the center — the most efficient surface.

A sphere is the 3D version of a circle: every point on its surface is the same distance (the radius) from the center. Soap bubbles, planets, marbles — when nature has the choice, it picks a sphere.

Volume
V = ⁴⁄₃ π r³
Surface area
A = 4 π r²

Among all shapes with the same surface area, a sphere encloses the most volume. That's why bubbles round up — surface tension is minimising the surface for the air inside.