Why Doesn't the Water Level Decrease When an Ice Cube Melts?

[Sam2847]

Consider a floating ice cube in a glass of water.

I know that the weight of the ice cube is equal to the weight of the water displaced.
This would mean that if the ice cube melted, the volume of water melted would be less than the volume of the ice cube, because ice has a lower density than water. As a result, the volume of water in the glass should decrease.

If this is the case, then why does the water level in the glass remain the same, rather than decreasing?

*Does it have something to do with the part of the the ice cube floating above water, which would account for the greater volume before melting? That way the total volume would still decrease after melting, but the water level would still remain the same.

 

[M Quack]

No, *yes

 

[algebrat]

does the water level change measurably if you submerge the ice with a safety pin?

 

[azizlwl]

Proposition 5 of Archimedes' treatise On Floating Bodies states that:

Any floating object displaces its own weight of fluid.
— Archimedes of Syracuse[2]

Volume displaced = volume submerged.
Volume displaced = ice converted to water. Since the weights are the same.