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This should be a simple question, but I haven't found a clear explanation anywhere yet.

Suppose that there are a bunch of particles in a gas, with their velocities "uniformly distributed over solid angles", and I want to find out what fraction of particles are traveling with velocities in a certain angular range.

Conceptually, I know what this means. I'm just not sure how to do it - I drew a diagram.

Suppose the shaded area represents 20% of the sphere's total surface area. How do find the angle theta?

Suppose that there are a bunch of particles in a gas, with their velocities "uniformly distributed over solid angles", and I want to find out what fraction of particles are traveling with velocities in a certain angular range.

Conceptually, I know what this means. I'm just not sure how to do it - I drew a diagram.

Suppose the shaded area represents 20% of the sphere's total surface area. How do find the angle theta?