The Area of a Sphere between Two Latitude Levels

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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 Θ₁>Θ₂.
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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dA = 2πr·Rdθ where r is the radius of the circular element and which is equal to r = Rcos(θ)

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

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

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