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Really quick general question but is upthrust independent of surface area. I came across the following:

"Heavy things can float on water if there is sufficient surface area to produce a big enough upthrust at a particular depth"

My thinking that this is incorrect is based on the assumption that whether or not something can float or sink is independent of everything except density because:

Upthrust = weight of displaced fluid = p V g = p (Ah) g

where p is density, V is volume, g is acceleration due to gravity, A is surface area and h is height

Weight = p(Ah) g

So upthrust and weight have identical terms except that the density 'p' is different in both. The 'p' in the weight terms is the density of the object whereas the 'p' in the upthrust term is the density of the fluid.

So increasing the surface area as far as I can tell would not help anything float because increasing it in the upthrust term will also increase it in the weight term. Lead sinks in water full stop. Surely lead can't float simply by increasing its surface area? The only way you would make lead float is to increase its effective density by hollowing it out with air.

Thanks for any comments!