The discussion focuses on calculating the volume of set S, which includes all points within a distance of 1 from a solid box defined by length L, width W, and height H. The formula for the volume of S incorporates contributions from the box's dimensions and the corners, resulting in the expression L*W*H + 2L*W + 2H*W + 2L*H + πH + πL + πW + (4/3)π. Participants express confusion about the origin of certain terms in the formula, particularly the π components. There is also curiosity about the volume generated by points inside the box at a distance of 1 from a specific point, suggesting a more complex function of three variables. Overall, the conversation highlights the challenges in understanding geometric volumes related to solid shapes.