percentage of volume?

Question

only a small part of an iceberg protrudes above the water, while the bulk lies below the surface. the density of the ice is 917 kg/m^3 and that of seawater is 1025 kg/m^3. find the percentage of the iceberg's volume that lies below the surface

Answer 1

The long way to demonstrate this is as follows:

Density = mass/volume.
Say you iceberg was V = 100 m^3, we know density is 917 kg/m^3.
Weight of the iceberg is mass = density * volume = 91700 kg.

The iceberg will displace an equal mass of water. So, the "hole" the iceberg makes in the ocean will be
V = mass/density = 91700/1025 = 89.5m^3

If the iceberg has 100 m^3 of volume, but only displaces 89.5m^3 of ocean then the amount under water = 89.5/100 = 89.5%

Answer 2

Archimedes Principle

P + B = 100%
P = (1025/917) - 1 = 11,777%
B = 88.223 %
The bulk that lies bellow the surface is the 88.223% of the iceberg.

Answer 3

In order for the ice berg to float, a sufficient amount of its volume must be submerged in order to displace enough water so that the buoyant force acting upward on the ice berg is equal to the total weight of the ice berg.
The buoyant force on the ice berg is equal to the weight of the displaced water.

Remember,
Density = mass / volume, which we can rearrange to get,
Mass = density * volume
and
Weight = mass * gravity

The weight of the ice berg can be found as,
Density of ice * total volume * gravity

The weight of the submerged water cab be found as,
Density of water * volume submerged * gravity

Setting these two quantities equal we get
Density of ice * total volume * gravity = Density of water * volume submerged * gravity
Since gravity appears on both sides we can cancel it out and get,
Density of ice * total volume = Density of water * volume submerged

Now to find the ratio of the submerged volume of the ice berg to the total volume we just rearrange the equation to be,
volume submerged / total volume = density of ice / density of water

The ratio the submerged volume of the ice berg to its total volume can be found as the ratio of the density of the ice to the density of the salt water it is floating in.

Plugging in for the values we know,
Ratio = (917 kg / m^3) / (1025 kg / m^3)
Ratio = .8946

So the percentage of the total volume of the ice cube which is submerged below the water is about 89.5% for the densities stated in the problem.