Question

What's the difference between a ball and a sphere?

Answer 1

A sphere is a two-dimensional surface embedded in three-dimensional space, while a ball is the interior of a sphere (which may or may not include the sphere itself).

A sphere and ball of radius r centered at the origin are respectively described by the equation and inequality,

x² + y² + z² = r²

and

x² + y² + z² < r²

or

x² + y² + z² ≤ r²