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Probably because volume increases faster than surface area.

Edit: To expand on that, assume the Queen Mary is an airtight cube. A small model of the cube might have 1m sides, with a volume of 1m³. If the real cube had sides of 3m, it would have a volume of 27m³. Buoyancy is a function of the volume of water displaced by an object, so since volume increases so much faster than surface area (and, by extension, weight), the larger cube would displace enough water to overcome its weight where the smaller one wouldn't.