A rather embarrassing (and stupid) question that nevertheless has managed totally stump me.

I build models, mainly aircraft but the odd ship too. As a kid I built a model of the Titanic at a scale of 1/350. The real thing was 269m (882ft) long and sure enough the model 77cm long (296/350). Fine.

However the real thing weighed in at 46,000 tons. So, 46,000/350 = 131 tons for the 77cm model, clearly something is amiss. Is it because the first calculation “works” effectively in 2D while the weight takes account of the 3rd dimension? i.e. I should be square rooting to the power of 3 and then dividing by the scale factor (1/350).

Any help is thoroughly appreciated (Ah the beauty of the internet, I can stay anonymous and not look like a prize muppet in front of colleagues…)