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QUESTION

# If silver has a density of 10.5 "g/cm"^3 and gold has a density of 19.3 "g/cm"^3, which would have the greater mass, 5 "cm"^3 of silver or 5 "cm"^3 of gold?

is defined as mass per unit of volume, which means that, for two substances that occupy the same volume, the more dense substance will weigh more.

In your case, silver has a of "10.5 g/cm"^3, which means that "1 cm"^3 of silver weighs 10.5 g; likewise, gold's desnity is given as "19.3 g/cm"^3, which means that "1 cm"^3 of gold weighs 19.3 g.

This means that, for equal volumes, the gold block will always weigh more than the silver block. The exact weighs of the two blocks will be

5cancel("cm"^3) * "10.5 grams"/(cancel("1 cm"^3)) = "52.5 g" -> the silver block

5cancel("cm"^3) * "19.3 grams"/(cancel("1 cm"^3)) = "96.5 g" -> the gold block

The gold block is heavier both because individual gold atoms are heavier than silver atoms, but also because they pack better - and that's what actually measures, how many atoms you can pack per unit of volume.

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