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The area of a sector of the sphere

Definition:

A sector of a sphere is a part of a sphere that is bounded by a curve surface of the spherical segment and conical surface, which serves as the base of the segment, and the apex – center of the sphere.

The area of a sector of the sphere is composed of the curve surfaces of the spherical and cone segments. Being known the radius of the base of the segment and cone r, with the Pitagora’s theorem and right triangle we can obtain the heigths of the segment and of the cone.

Computing relationship:

for:

where:

r1 — the radius of large circumference (sphere);

r2 — the radius of small circumference (base).

Calculator: the area of a sector of the sphere


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

the radius of large circumference (sphere) — r1

the radius of small circumference (base) — r2

 


the area of a sector of the sphere =

 

 

context information: contemporary and archaic unit of measurement of area