An iceberg is floating partially immersed in sea water. The density of sea water is `1.03 g cm^(-3)` and that of ice is`0.92 g cm^(-3)`. The approximate percentage of total volume of iceberg above the level of sea water is

Options

A. `8`
B. `11`
C. `34`
D. `89`

Explanation

To solve the problem of determining the approximate percentage of the total volume of an iceberg that is above the level of seawater, we can follow these steps:

### Step 1: Understand the relationship between the densities and volumes
When an object floats, the weight of the object is equal to the weight of the fluid it displaces. This can be expressed as:
\[ \text{Weight of Iceberg} = \text{Weight of Displaced Water} \]

### Step 2: Define the variables
Let:
- \( V \) = total volume of the iceberg
- \( x \) = volume of the iceberg submerged in water
- \( \rho_{\text{ice}} \) = density of ice = \( 0.92 \, \text{g/cm}^3 \)
- \( \rho_{\text{water}} \) = density of seawater = \( 1.03 \, \text{g/cm}^3 \)

### Step 3: Write the equation for buoyancy
The weight of the iceberg can be expressed as:
\[ \text{Weight} = \rho_{\text{ice}} \cdot V \cdot g \]
The weight of the displaced water can be expressed as:
\[ \text{Weight} = \rho_{\text{water}} \cdot x \cdot g \]
Setting these equal gives:
\[ \rho_{\text{ice}} \cdot V = \rho_{\text{water}} \cdot x \]

### Step 4: Relate submerged volume to total volume
From the equation above, we can rearrange to find the ratio of submerged volume to total volume:
\[ \frac{x}{V} = \frac{\rho_{\text{ice}}}{\rho_{\text{water}}} \]

### Step 5: Substitute the known densities
Substituting the values for the densities:
\[ \frac{x}{V} = \frac{0.92}{1.03} \]

### Step 6: Calculate the submerged volume ratio
Calculating the above gives:
\[ \frac{x}{V} \approx 0.8922 \]
This means approximately 89.22% of the iceberg's volume is submerged in water.

### Step 7: Calculate the volume above the water level
The volume of the iceberg above the water level is:
\[ V_{\text{above}} = V - x = V - 0.8922V = (1 - 0.8922)V = 0.1078V \]

### Step 8: Calculate the percentage of volume above the water level
To find the percentage of the total volume that is above the water level:
\[ \text{Percentage above} = \left(\frac{V_{\text{above}}}{V}\right) \times 100 = 0.1078 \times 100 \approx 10.78\% \]

### Step 9: Round to the nearest option
Rounding 10.78% gives approximately 11%.

### Final Answer
The approximate percentage of the total volume of the iceberg above the level of seawater is **11%**.

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