Do Density Tests Really Work

I was wondering if density tests work as I have seen that you can hang a coin from a string using a balance scale then weigh the coin dry then put it in distilled water at 70 degrees and weigh it again, subtract the difference and divided this number into the dry weight this is to be the density? Why you say do you ask well I took a silver coin and did this and I came up with a density of 8.76 I thought silver was to be 10.4 I had same melted down lead and I do not know how pure it was but it's density was 11.10 seems kind of right just wondering if this is the way they tell if metals are made of what they say they are made of?

John