Spherical sector

A cone with its apex at the centre of a ball, capped by the sphere: an ice-cream cone shape.

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Units

Dimensions

sphere radius r1.8cap height h0.8

Results

volume V

Formulas

Each point of the cap surface sees the centre along a thin pyramid of height r: volume = (cap area 2πrh) × r / 3.

Checked: the V 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.