# Homework Help: If an ice cube floating in a glass of water melts, won't the water level decrease?

1. Jun 16, 2012

### 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.

2. Jun 16, 2012

### M Quack

Re: If an ice cube floating in a glass of water melts, won't the water level decrease

No, *yes

3. Jun 16, 2012

### algebrat

Re: If an ice cube floating in a glass of water melts, won't the water level decrease

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

4. Jun 16, 2012

### azizlwl

Re: If an ice cube floating in a glass of water melts, won't the water level decrease

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.