What is the Submerged Volume of a Styrofoam Cube in Water?

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To determine the submerged volume of a 10g styrofoam cube in water, it's essential to understand that it must displace an equivalent weight of water. Given that the density of water is 1g/cm³, the cube needs to displace 10cm³ of water to float. With a base area of 100cm², the height of the submerged portion is calculated to be 1mm. This confirms that the styrofoam cube will indeed be submerged by 1mm in water. The discussion highlights the application of Archimedes' principle in practical scenarios.
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I'm trying to find how much of a cube of styrofoam is submerged in water without measuring because the amount is very small.

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If I have a block of styrofoam with a mass of 10g and a density of 0.018g/cm3
How much of the styrofoam will be submerged?
 
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MY guess would be 1mm, 10g of water has a volume of 10cm^3, so the same volume of styrofoam to displace same volume of water would be .1cm *10 cm * 10cm
 
I'm a little bit confused. Can you explain that again more thoroughly?
 
Any floating object displaces its own weight of fluid.

— Archimedes of Syracuse[3]

So the weight of the styrofoam is 10g, to float, it must displace 10g of water

The density of water is 1g/cm^3 so 10g of water has a volume of 10cm^3. That is the volume of water to be displaced by an equal volume of styrofoam, since the block has a 100cm^2 bottom, it will take a height of 1mm to reach the desired volume.
 
Wow, simple. thanks!
 

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