Re: What is the most efficient container shape?

While it sounds both flip and unhelpful, the most efficient container shape is the one which will best do the job.

Of course, this begs the question of "what job do you want to do?" If you are trying to pack something which has a particular shape, then you need to adapt your container to that shape as well as to the considerations mentioned below.

If you want to contain something without a particular shape of its own, and minimize the amount of packaging material used, a sphere is the most efficient: it has the lowest surface-to-volume ratio of any geometric solid, and "round" containers are generally used for any application requiring great strength.

However, a sphere stacks rather less efficiently than it packs, since stacking spheres leaves you with lots of unavoidable empty space between containers. This means that if you are trying to pack something into multiple containers, the sphere will not be the most efficient shape. You'd be better off with some sort of rectangular parallelepiped: think about stacking blocks vs. stacking balls. The blocks stack with less space between them. This is why most real-world packaging is, well, box-shaped rather than spherical.

And anyhow, spheres have all sorts of other engineering problems associated with them. For one thing, they roll away unless you brace them in place; this is one reason (the other is ease of fabrication) that grain bins and liquid storage tanks are usually cylinders rather than spheres.

In application, I have seen (as an example) bulk sodium chloride (table salt) packed both in parallelepipeds and in cylinders. The parallelepipeds stack more efficiently, but the cylinders are much more resistant to crushing. You will notice that all high-pressure gas containers are cylinders - and usually cylinders with at least one end rounded for extra strength.

In general, although spheres are the most efficient shapes for packing things into, they do not pack very efficiently themselves. So a container is usually a compromise between strength (sphere) and stackability (parallelepiped).