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Does juice box have a surface tension?
No. Surface tension is a characteristic of liquids, not solids like a juice box.
What is the measurement describing the number of unit squares that cover a surface?
That's the area of the surface.
What is a measurement describing the unit squares that cover a surface?
area
What has to have more density for an object to float on water the object or water?
Normally the water - to float and object has to displace a volume of water equal to its mass. If its density is greater than that of water, the maximum mass of water it can displace is its own volume which, as the water is less dense that it, will have less mass than the object and it will sink. However, for small light objects the surface tension of water comes into play - it is possible to float a steel sewing needle (with a density greater than water) on water by gently dropping a clean needle on its side onto the water surface so that it does not break the surface tension. With a needle floating, adding a few drops of washing up liquid to the surface reduces the surface tension and the needle will then sink.
How could it be possible that an object with a density greater than that of water could float in water?
There are two ways to make an object with a density greater than water float on it: 1) reduce its density, for example by hollowing it out or adding further structures with a density [much] less than that of water so that it can displace a volume of water equal to its own weight and still have some of its structure above the surface of the water; or 2) Use the surface tension of water so that the object floats - dropping a steel sewing needle on its side very gently onto water will prevent it breaking the surface tension of the water and it will float, until such time as the surface tension is broken, eg by adding a few drops of washing up liquid or agitating the surface, when the needle will sink. (The needle needs to be clean.)
