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The volume of the spherical segment

Definition:

A 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 volume of the spherical segment is equal to the product of the value Pi, square of the height of the spherical segment and the difference between the radius of the circumference obtained as result of sectioning and a third part of the segment.

Computing relationship:

where:

r — the radius of large circumference (sphere);

h — the height of a sphere segment.

Calculator: the volume of the spherical segment


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

the radius of large circumference — r

the height of a sphere segment — h

 


the volume of the spherical segment =

 

 

context information: contemporary and archaic unit of measurement of area