1. The problem statement, all variables and given/known data A 12 foot light pole stands at the corner of an 8 foot by 10 foot rectangular picnic blanket spread out on the ground. A bee flies in a straight line from a point P on the pole to a point Q on the blanket. Set up a multiple integral whose value represents the average length of all possible paths along which the bee could fly. 2. Relevant equations None so far. 3. The attempt at a solution After sketching the situation, I think spherical coordinates would be best to use, but I am having trouble figuring out the bounds. I think that rho would go from sqrt(12^2+8^2) to sqrt(12^2+10^2+8^2), these being the shortest and longest length of rho from the top of the pole to the corners of the blanket. This would only give half of the region of the blanket though. If i could find an integral and multiply it by 2, it should work. If this were the case, theta would go from 0 to pi/2. My main issue would be finding the values for phi. I would imagine it would go from (pi/2)+tan^-1(12/sqrt(10^2+8^2) to pi. My other concern is that maybe rho has to be a function of phi somehow. Sorry for the confusing description, but this problem is giving me a lot of issues. Any advice to point me in the right direction would be immensely appreciated! Thank you!