Archimedes Principle of Buoyancy

Question:
If a penny is tossed into the ocean will it displace more or less water than the same penny placed on the deck of a boat?

Answer:
The penny placed on the deck will displace more water.

The penny in the ocean will displace its volume while the penny on the deck will displace its mass. We know that the penny is more dense than water because it sinks to the bottom of the ocean.

Approximate density of a pure copper penny: 8.92 g/mL
Approximate density of water: 1 g/mL

Approximate volume of a penny: 0.360 mL
Approximate weight of a penny: 3.21 g

When the penny is placed on the deck it must displace its weight in the water. Therefore the penny must displace 3.21 g of water, which is equivalent to 3.21 mL of water. The penny at the bottom of the ocean is only displacing 0.360 mL of water. So more water will be displaced due to the weight of the penny than its volume.

We know,

If we allow Vp and Vw to represent unit areas and decrease the volume to account for less mass,

where

result,    or,

The volume of the displaced water is more than the volume of the penny.