"Rebel 1" axes in message
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I posting this here because there a good analytical minds here.

An experiment: Fill a tall clear glass half-way(sic) with ice cubes. Then
add enough water so the bottom cubes no longer touch the bottom (i.e.,
they are all floating). Now put a mark at the water level and wait until
the cubes all melt. Did the water rise above your mark?

In my case, it didn't.

R1

Different scenario. Some of the melting ice is sitting on land and will
be added to the sea in the form of water.

Repeat your experiment filling the glass with ice, add water to the rim.
Now set a couple more cubes on the rim of the glass. That is closer
to what may eventually happen.