Other Properties
Since A = r2, it corresponds to the area of a spherical cap (A = 2πrh) (wherein h stands for the "height" of the cap), and the relationship h/r = 1/(2π) holds. Therefore one steradian corresponds to the plane (i.e. radian) angle of the cross-section of a simple cone subtending the plane angle 2θ, with θ given by:
This angle corresponds to the plane aperture angle of 2θ ≈ 1.144 rad or 65.54°.
A steradian is also equal to the spherical area of a polygon having an angle excess of 1 radian, to 1/(4π) of a complete sphere, or to (180/π)2 ≈ 3282.80635 square degrees.
The solid angle in steradians of a cone whose cross-section subtends the angle 2θ (θ shown in the image) is:
More intuitively expressed as a "surface area" of the cone's angle:
For small angles when θ is in radians using sin(A)~A:
Read more about this topic: Steradian
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“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
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—John Locke (1632–1704)