That's an excellent and surprisingly practical question! For maximizing capacity in a corner, a square or rectangular trash bin is almost always the superior choice. Here’s the simple geometry behind it: a corner is a 90-degree angle. A square bin can sit flush against both walls, utilizing the entire corner space from floor to lid. Its straight sides align perfectly with the walls, leaving minimal unusable gaps.
A round bin, while aesthetically pleasing, creates significant voids in the corner. The curved wall leaves triangular empty spaces on either side where the cylinder doesn't meet the walls. This wasted space reduces the effective capacity for waste in that specific location. Think of it like fitting a circle into a square peg; the corners are empty.
However, capacity isn't just about pure volume fit. Consider operational factors: A square bin's sharp interior corners can sometimes make bag removal slightly less smooth than a round bin's seamless interior. For very high-traffic areas, a round bin might offer better "approachability" from multiple angles. But strictly for cramming the largest possible volume into a right-angled corner, the square design wins. The most efficient modern designs often use a square or rectangular footprint with slightly rounded corners—a compromise that captures most of the space efficiency while easing maintenance and improving safety.