While reading The Thinking Body by Mabel Todd today, I came across the statement, cribbed from Human Anatomy by Geroge Arthur Piersol, that "a given quantity of matter is much stronger, both lengthwise and crosswise, when disposed in a hollow cylinder than as a solid one of equal size and length."

Well, this seemed like a fuzzy statement of the setup to me. As they said in The Giver: precision of language, people! Precision of language! There are three different cases here, all slightly different.

1. Given the same amount of stuff - imagine two identical lumps of clay - and having to support, say, the same book at the same height with each lump. Between building a solid cylinder to hold up the book, and forming the clay into a hollow (and therefore larger-diameter, because it's the same amount of clay) cylinder to hold up the book, you'll get stronger results from the hollow cylinder in general. They'll be identically strong in compression (book-pressing-straight-down-on-column) but the cylinder will have a broader base, which is going to make it more stable. The cylinder will also be stronger bending-wise because the moment of inertia will be bigger.
2. Given a hollow cylinder and a solid one of equal size and length - imagine two identical solid metal cylinders, and drilling a hole straight through one of them so it becomes a tube - the solid cylinder will be stronger both in compression (more "stuff" to bear the load") and bending-wise (again, more "stuff" you have to bend). However:
3. Mass-to-strength ratio-wise, hollow cylinders win hands-down. You can do the calculations if you like (I do not particularly feel like calculus at the moment, but could do it if I had to). If you take a cylinder of stuff and drill out 50% of the material from its inside, so that it's a hollow tube, you've lost half the weight, but only something like 10% of the strength. I think it's because one of them depends on the square of the drilled-out radius, and the other on the cube, or somesuch.

Yes, I know that last sentence will be unsatisfyingly fuzzy for some. There's a nice discussion here
with more formulas for those who like their physics with more rigor, and on another day I might have gone down that path myself, but I'm satisfied enough with this to keep on reading about the
structural properties of the human skeleton - the "hollowness" of bones -
which are filled with marrow, they're not actually hollow - was what
prompted that sentence in the first place. Now I can move on with life and move on to learn about
how tendons and ligaments restrict the range of motion of a joint.
Woohoo!