Final answer:
Without specific density values, only charcoal can be confidently said to float in molten lead as it usually has a very low density, and the other materials might sink.
Step-by-step explanation:
To determine which materials would float in a molten vat of lead, we need to compare the densities of the materials in question. A substance will float in a liquid if its density is less than the liquid's density. According to the information provided about the densities of various substances, we can understand that gold has a density of 19.3 g/cm³, which is higher than that of lead, suggesting that gold would sink in molten lead. No information about the densities of platinum, glass, or charcoal is provided, but in general, charcoal typically has a very low density due to its porous structure, and it would likely float on molten lead. On the other hand, platinum and glass both tend to have high densities, which makes them less likely to float, but without specific density values, a definitive determination can't be made. Therefore, the materials that would float in molten lead are charcoal and potentially glass, depending on its density relative to lead.