Work out spherical cap instantly with clear inputs, formula shown and shareable results.
Slicing a sphere with a plane leaves a cap of height h. Its volume is ⅓πh²(3R − h) and — remarkably — its curved area 2πRh depends only on the slice thickness, not on where the cut is made.
Cap volume
V = ⅓πh²(3R − h)
Curved area
A = 2πRh
Base radius
a = √[h(2R − h)]
The formula gives ⅔πR³, the hemisphere, as it must.
This is Archimedes' hat-box theorem: equal-thickness slices of a sphere have equal curved surface areas.