The way the question is posed, it seems to me that the radius R of hollow spherical shell should not figure in the calculation. Assume there is no Earth, and y

The way the question is posed, it seems to me that the radius R of hollow spherical shell should not figure in the calculation. Assume there is no Earth, and you are hanging out in the center of a large hollow sphere. In that case, you can see 100% of that sphere, no matter how large it is. Now, let's say that earth magically appears, and now r' varies from 0 to r. The question asks to find percentage of the sky visible as a function of r'