Metallurgy is pretty interesting indeed. I've done some forging of knives myself so I've spent a couple of hundred hours researching steels. Made some damask steel myself too, that shit takes way too long to forge but man is it pretty when you cut and polish it. The upside to taking long to forge is that it doesn't require any specific high-grade tools unlike modern supersteels.
Oh, random fact about japanese katanas, you know how they always promote the "folded so and so many times"? The more you have to fold it, the shittier your iron ore was to begin with. And any folding after the seventh time or so means your katana sucks. The gains after that point degrades the metal and is more for aesthetic purposes.
It's funny though, the japanese didn't even know what steels was before the Europeans brought the concept over. Chinese invented steel back in the BCs which makes it even funnier. The knowledge had to make a full round circle of the earth before reaching the island nation. Of course part of the reason is that the Japanese iron ore is total crap, which is why the katana is as it is, you could not forge it from one piece or it would simply break apart in battle. The backside keeps the hard edge from shattering on impact, or it's supposed to. Even the "final" form of katana can be broken apart rather easily by anyone having decent skill with sai or the japanese baton. You hit the sword straight on to chip away a part of the blade and then simply twist your weapon to break apart the sword, higher quality katanas could require two hits to the same spot first. So yeah, the katana is not the form it is because it is the ultimate form, it's the way it is so that you can make it from japanese iron and it won't break apart at first contact.
Again, it also depends if you are talking about strength by weight or strength by volume.
I always assume people comprehend strenght as by volume. That is how we normally handle stuff in day-to-day life. 2x4, 5inch pipe etc.
Weight is only relevant for more abstract stuff like engineering calculations and stuff.