The following is a beautiful image of an iceberg depicting the portion above water and the portion below water that is typically hidden from view. Aside from its beauty, what's astonishing about this image is how large a fraction of the volume of the iceberg is under water. In this problem sequence, we show why so much of the iceberg's volume is below the surface. Throughout, we note that icebergs are typically composed of freshwater (nearly pure), while the surrounding liquid water is typically saltwater. The density of liquid saltwater is about 1027 kg/m3.

2.1. If you put 900 mL of liquid freshwater into a large plastic bottle and then put that bottle into a freezer to turn the water to ice, you'll end up with 1000 mL of ice in the bottle1. What is the density of freshwater ice?

2.2. Let V be the total volume of an iceberg, and let VS be only the volume submerged under water. Let ?I be the density of freshwater ice, and let ?S be the density of liquid saltwater. Show that

VS/V=?I/?S

2.3. Based on the equation derived in the previous question, what percent of an iceberg's volume would we predict

is submerged under water? Make sure your answer seems reasonable given the iceberg picture.