Reckoning / Shape / Spherical cap (segment of one base)
Solid · Spheres
Spherical cap (segment of one base)
The piece of a ball cut off by one plane, like a dome.
Drag to turn · pinch or scroll to zoom
Dimensions
Results
volume V
curved surface L
base radius a
Formulas
Archimedes’ hat-box theorem: the sphere’s surface between two parallel planes equals the side of the enclosing cylinder between them, 2πr times the height.
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.