Sinking a Cup With Pennies

My daughter is studying mass, volume and density this week.  I created this lab experiment for her class.  A Styrofoam cup has a mass of 3.5g and a volume of 60 cm3.  If you hold the cup under water and release it, it will float to the surface.  What is the minimum number of U.S. pennies needed to put into the cup to keep the cup from floating?

Extension: The class actually has to determine the mass and volume of the cup.  How would you find the volume of Styrofoam in a Styrofoam cup?

Source: Original.

Solutions were received from Joseph DeVincentis and Kirk Bresniker.  Joseph was the first to see the trick in the question - U.S. pennies changed their mass in 1982.  Prior to 1982, pennies were made primarily of copper and had a mass of about 3.1 grams.  Pennies made after 1982 are composed primarily of zinc, and have a mass of about 2.51 grams.  Older pennies weigh more, so we'll use those.  The volume of a penny is 0.36 cubic cm.  Water has a density of 1.  We need to find the density of the Cup & Pennies:(Total Mass / Total Volume) to be greater than 1.

( 3.5 + N*3.1) / (60 + N*.36) = 1

Solving for N = (VolumeCup-MassCup)/(MassPenny-VolumePenny) = 20.62

So 21 pennies (dated older than 1982) would sink the cup.  For comparison, 27 newer (than 1982) pennies would be needed.

To find the volume of the cup, a few suggestions were made:
1) Perform the experiment with the pennies, then back-calculate the volume of the cup.  (This is probably the most accurate.)
2) Get a graduated cylinder large enough to hold the cup and insert the cup in until it is just at the level of the water.  The water level will increase equal to the "outside volume" of the cup.  Then fill the cup and measure the "inside volume" of the cup.  Subtract to find the cup's volume.
3) Completely submerge the cup into water in a graduated cylinder and measure the water level increase.  The increase in milliliters is equal to the cup's mass in cubic centimeters.  (This is how the students did it in the lab.)

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