Does submerging a cup measure its volume or its volume plus trapped air?

[cp3themvp]

If I submerge a cup in a graduated cylinder filled with water, will the change of the water line show me the volume of the cup? Or is this not the case?

I am in an argument with a friend, he believes that the volume of the cup could be found by holding the top of the cup right about the water line(in other words, not allowing any water to enter to the cup) and then measuring the change of the water line. I argued that if one uses this method of measurement, that the change in the water line now includes the volume of the air that is inside of the cup.

The scientific definition of volume I found is the amount of space an object takes up. In the 1st experiment I proposed, I believe this finds the amount of space the cup takes up. In the 2nd experiment, I believe this finds the amount of space the cup takes up+the amount of space the air inside of the cup takes up. Am I correct, or is the 2nd experiment actually the correct method for measuring the volume of a cup?

 

[fresh_42]

You are right, drown the cup. There is a famous story about this experiment:
http://www.longlongtimeago.com/once-upon-a-time/great-discoveries/eureka-the-story-of-archimedes-and-the-golden-crown/

 

[Drakkith]

I am in an argument with a friend, he believes that the volume of the cup could be found by holding the top of the cup right about the water line(in other words, not allowing any water to enter to the cup) and then measuring the change of the water line. I argued that if one uses this method of measurement, that the change in the water line now includes the volume of the air that is inside of the cup.

The scientific definition of volume I found is the amount of space an object takes up. In the 1st experiment I proposed, I believe this finds the amount of space the cup takes up. In the 2nd experiment, I believe this finds the amount of space the cup takes up+the amount of space the air inside of the cup takes up. Am I correct, or is the 2nd experiment actually the correct method for measuring the volume of a cup?

This is an issue of wording. By 'volume of the cup' do you two mean the volume of fluid that the cup can hold? Or do you mean the volume of the material composing the cup? The former would require that you just fill the cup with fluid and pour it into a graduated cylinder. The latter is found by submerging the entire cup, not just submerge it until the water reaches the rim.

 

[A.T.]

The scientific definition of volume...

Don't waste your time on arguing about definitions. Just clarify which volume you both mean and use qualifiers to distinguish them. It depends on the application which volume is the relevant one.

 

[ZapperZ]

If I submerge a cup in a graduated cylinder filled with water, will the change of the water line show me the volume of the cup? Or is this not the case?

I am in an argument with a friend, he believes that the volume of the cup could be found by holding the top of the cup right about the water line(in other words, not allowing any water to enter to the cup) and then measuring the change of the water line. I argued that if one uses this method of measurement, that the change in the water line now includes the volume of the air that is inside of the cup.

The scientific definition of volume I found is the amount of space an object takes up. In the 1st experiment I proposed, I believe this finds the amount of space the cup takes up. In the 2nd experiment, I believe this finds the amount of space the cup takes up+the amount of space the air inside of the cup takes up. Am I correct, or is the 2nd experiment actually the correct method for measuring the volume of a cup?

This can easily be clarified by specifying if you want the volume of the MATERIAL that forms the cup, or do you want the volume that the cup can hold.

These are two different definitions and give two different volumes.

By submerging the cup in water and making sure that there are no air pockets, you are measuring the volume of material that forms the cup. By filling the cup up to the brim with water and then measuring that volume of water, you are measuring the volume that the cup can hold.

Zz.

 

[A.T.]

This can easily be clarified by specifying if you want the volume of the MATERIAL that forms the cup, or do you want the volume that the cup can hold.

I think the method suggested by the OP's friend is a third variant: the sum of the two volumes above. This would be relevant if you plan to use the cup as a boat, and want know its maximal displacement.