San José State University

applet-magic.com
Thayer Watkins
Silicon Valley
& Tornado Alley
U.S.A.

The Area of a Sphere between
Two Latitude Levels

Let the sphere be of radius R and the two latitude levels Θ1 and Θ2, with Θ12.

The infinitesimal element dA of the spherical area is

dA = 2πr·Rdθ
where r is the radius
of the circular element
and which is equal to
r = Rcos(θ)

Thus

A(Θ) = ∫2πR²cos(θ)dθ = 2πR[sin(θ)]
and hence the area
between Θ1 and Θ2 is
2πR²[sin(Θ2)−sin(Θ2]


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