1. The problem statement, all variables and given/known data Consider a solid box with dimensions L,W, and H. Let S be the set of all points whose distance is at most 1 from the nearest point inside or on the box. What is the volume of S? 2. Relevant equations Not sure if there are any? 3. The attempt at a solution My initial thought was that S would be a sphere within the box, but after thinking over the problem for a bit, I don't think that's the case. I think my biggest problem here is that I can't imagine the shape of S, so figuring out what to do mathematically is confusing me. I next thought maybe S was a cube within the box, but that doesn't sound right either.