A collection of 100 identical marbles having a total mass of 125g are poured into a graduated cylinder and found to come up to the 100-cm^3 mark. When the marbles are added to 75cm^3 of water in a...

A collection of 100 identical marbles having a total mass of 125g are poured into a graduated cylinder and found to come up to the 100-cm^3 mark. When the marbles are added to 75cm^3 of water in a second graduated cylinder, the water level rises to the 137-cm^3 mark. 

- what is the volume of the marbles alone, in cm^3?

-what is the volume of the air space between the marbles?

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t-nez | High School Teacher | (Level 3) Associate Educator

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Let's start with the volume of the marbles. Water displacement is a common way to find the volume of irregularly shaped objects. The amount by which the level of the water rises when an object is submerged is the amount of water displaced by the object and is equal to its volume. The marble displaced 62 cm^3 of water, the difference between the final volume of 137 cm^3 and the initial volume of 75 cm^3. Therefore the volume of the marbles is 62 cm^3.

The volume of the air space around the marbles is the amount of space the  marbles filled in the graduated cylinder minus their actual volume. So out of the 100 cm^3 that the marbles occupied, 62 cm^3 is the marbles and 100-62 = 38 cm^3 is the volume of air space surrounding the marbles.

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