Spherical zone (segment of two bases)

The slice of a ball between two parallel planes.

Drag to turn · pinch or scroll to zoom

Units

Dimensions

sphere radius r1.8lower plane z₁ (from centre)-0.6upper plane z₂ (from centre)1.0

Results

volume V

zone surface L

Formulas

The curved surface depends only on the thickness h, not on where the slice is taken: the hat-box theorem again.

Checked: the V, L formula agrees with a Monte Carlo measurement of the shape itself, made from its geometric definition, every time the site is built.

Topology lens

Topologically a ball: its surface can be stretched onto a sphere without tearing, so its Euler characteristic is 2. More on the lens.