Final answer:
The percentage of the iceberg's volume that is under water is 89%.
Step-by-step explanation:
To find the percentage of the iceberg's volume that is under water, we need to compare the density of ice to the density of seawater. The volume of the iceberg is given as 100000 ft³ and the density of pure ice is 57.2 lb/ft³. Since the iceberg is floating, it displaces its own weight in water. So, the weight of the iceberg is equal to the weight of the water it displaces. We can use the equation ρ = m/V, where ρ is density, m is mass, and V is volume, to find the mass of the iceberg. The density of seawater is 64.3 lb/ft³. Using these values, we can calculate the mass of the iceberg as follows:
m = ρV = (57.2 lb/ft³)(100000 ft³) = 5,720,000 lb
Now, since the volume of water displaced by the iceberg is equal to its own volume, we can find the volume of water submerged by dividing the mass of the iceberg by the density of seawater:
V_submerged = m/ρ_water = (5,720,000 lb)/(64.3 lb/ft³) = 89,000 ft³
Finally, to find the percentage of the iceberg's volume that is under water, we divide the volume submerged by the volume of the iceberg and multiply by 100:
Percentage submerged = (V_submerged/V_iceberg) × 100 = (89,000 ft³/100,000 ft³) × 100 = 89%