1. Sep 17, 2014

jmc

1. The problem statement, all variables and given/known data
For a sphere of radius r, find the solid angle Ω in steradians defined by spherical angles
of: a.) 0°≤θ≤ 20°, 0°≤ø≤360°;

2. Relevant equations
dA = r2 sin dθ dø (m2)
dΩ = dA / r2 = sin dθ dø (sr)

3. The attempt at a solution
I think I understand what a steradian (sr) is, on a sphere, and I need to find what ratio of a 4∏ is formed by the above limits, but I can't make the connection on how to form that ratio. ?

2. Sep 17, 2014

SteamKing

Staff Emeritus
First, draw a sketch of the region. I assume you are familiar with spherical coordinates?

3. Sep 17, 2014

jmc

I have tried to sketch it. What I see is.the top portion of the sphere, sliced where 20 deg from the X-axis meets the edge of the sphere.
But how to convert that to a steridian, I still don't see.

Thank you

4. Sep 18, 2014

SteamKing

Staff Emeritus
You have to go back to the definition of what the steradian represents:

You do not need to take any ratio. You simply have to integrate $d \Omega$ over the section you are considering.