Find density of copper and with graduated cylinders and water?

The way I did it was to first measure the mass of the piece of copper.
Fill the graduated cylinder with water until it's a little more than the length of piece of copper.
Put the copper in a read the measurement.
Take the volume of the water with copper and subtract the volume of the water originally to find the volume of copper.
And to find the density, I just take the mass divided by volume.
And are those all I need to do to find the density of copper? Is there anything else that I need to consider like the volume or density of water?

Answer:
What you did sounds close to the procedure in these lesson plan for the "Penny Density Experiment" and "making Cents of Density http://www.wmich.edu/engineer/ceee/page/... and this http://www.cmu.edu/gipse/materials/pdf-2...
Read to see if you missed anything.
That is all you need to do. The volume/mass/density of the water is taken as a constant, so since it is the same across the two volume readings, it cancels out when you subtract the initial and final volumes.

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