In order to resolve this, we'll need to apply several principles from chemistry and physics - specifically, some related to mass, density, and buoyancy.
1. We begin by calculating the volume of the iceberg using the formula Volume=mass/density. The mass of the iceberg is given as 6 * 10^9 kg, and the density of the iceberg is 1000 kg/m³. This gives us the volume of the iceberg.
2. Next, we can calculate the height of the iceberg by dividing the volume by the product of length and width (30 meters * 40 meters) of the iceberg.
3. Now, we can apply the Archimedes' principle to calculate the part of the iceberg that is underwater. Archimedes' principle states that "an object submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object." Using the formula: underwater height = iceberg height * (iceberg density / sea water density), we get the underwater height of the iceberg.
4. To calculate the part of the iceberg above water, we subtract the underwater height of the iceberg from the total height of the iceberg.
5. In order to determine how many penguins can sit on the top of this iceberg without the iceberg becoming completely submerged, we need to calculate the mass of the ice underwater when the iceberg is completely submerged, which is max_mass = underwater height * iceberg length * iceberg width * sea water density.
6. After calculating the max_mass, we subtract the actual mass of the iceberg from max_mass and get the remaining mass capacity of the iceberg. Then we divide this mass by the mass of a penguin to get the number of penguins that the iceberg can accommodate.
After performing the above steps:
a) The part of the iceberg that is underwater is approximately 4878.05 meters.
b) The part of the iceberg that is above the water is approximately 121.95 meters.
c) As the mass of the iceberg is already equal to the maximum mass it can handle while staying afloat, no penguins can sit on the top of this iceberg before it becomes completely submerged. So the answer is 0.0.