Imagine viewing a hemisphere normal to the equator such that it looks like a circile with the full radius of the hemisphere. Now randomly section or cut the hemisphere in a manner a tomato is sliced. If we only consider the portion of the hemisphere that contains the pole we should be generating a smaller radius then the full radius given we actually cut something off. My question is the following: What is the average length of the radius of a randomly cut cross-section? I did this numerically and obtained 0.7855 of the original radius. What is the analytical approach? Thanks.