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The area of a spherical segment or of a spherical calotte

Definition:

The spherical segment or spherical calotte is a part of a sphere sectioned by a surface. The circle ABCD is the base of the segment. The height of the segment is the segment NM, that is, the length of the perpendicular initiated from the center N until the intersection with the sphere surface. The point M is called as apex of the spherical segment.

The area of a spherical segment or of a spherical calotte is equal to the doubled product of the value Pi, height of the segment and the radius of sphere.

Computing relationship:

where:

r — the radius of a sphere;

h — the height of a sphere segment.

Calculator: the area of a spherical segment or of a spherical calotte


For separation of number integers and decimals, use the symbol – point [.]

the radius of a sphere — r

the height of a sphere segment — h

 


the area of a spherical segment =

 

 

context information: contemporary and archaic unit of measurement of area