Measuring Solid Angle of Cuboid: Steradians

[Atran]

Hi, How can I measure one solid angle of a cuboid, at least a non-sphere shape?
I've read about steradians on internet, so I haven't studied it in any textbook.

Thanks...

 

[Atran]

A cuboid with the sides (a), (b) and (c).
I think the total steradians of it is 360²=(129600*π)/360=720π

V = a*b*c
V = (4π(r³))/3

((3*a*b*c)/4π)^(1/3) = r
((3*a*b*c)/4π)^(2/3) = r²

((3*a*b*c)/4π)^(2/3) * 720π = A

Is that procedure correct?

 

[Atran]

I think the total steradians of it is 360²=(129600*π)/360=720π

I wrote incorrect above, right?
If a circle and a rectangle have totally 360 degrees, therefore a sphere has the same amount of degrees (4π) as a cuboid has.

So this should be incorrect ((3*a*b*c)/4π)^(2/3) * 720π = A),
and the correct one should be: ((3*a*b*c)/4π)^(2/3)) * 4π = A

All I want is to measure one point's degrees in a cuboid.

 

[g_edgar]

Don't use 360^2. That would be stedegrees or something. Not steradians.

 

[CellCoree]

Hello, measuring the solid angle of a cuboid can be done by using the concept of steradians. Steradians are a unit of measurement for solid angles, similar to how degrees are used to measure angles in a plane. To measure the solid angle of a cuboid, you can use the formula: solid angle = area of the face / distance^2. This formula takes into account the surface area of the face of the cuboid and the distance between the observer and the face. You can use this formula for each face of the cuboid and then add up the individual solid angles to get the total solid angle of the cuboid. It is important to note that the solid angle of a cuboid will vary depending on the orientation of the observer and the distance from the cuboid. I hope this helps, and I would recommend further research or consulting a textbook for a more in-depth understanding of steradians and solid angle measurements.