An iceberg of density `900kg//m^(3)` is floating in water of density `1000 kg//m^(3)`. The percentage of volume of ice cube outside the water is

Options

A. 20
B. 35
C. 10
D. 11

Answer

To solve the problem of finding the percentage of the volume of an iceberg that is outside of the water, we can follow these steps:

### Step 1: Understand the Problem
We have an iceberg with a density of \( \rho_{\text{ice}} = 900 \, \text{kg/m}^3 \) floating in water with a density of \( \rho_{\text{water}} = 1000 \, \text{kg/m}^3 \). We need to find the percentage of the iceberg's volume that is above the water surface.

### Step 2: Define Variables
Let:
- \( V \) = Total volume of the iceberg
- \( V_1 \) = Volume of the iceberg submerged in water
- \( V_2 \) = Volume of the iceberg above the water surface

From the definition of volume, we have:
\[ V = V_1 + V_2 \]

### Step 3: Apply the Principle of Buoyancy
According to Archimedes' principle, the weight of the water displaced by the submerged part of the iceberg is equal to the weight of the iceberg itself. Therefore, we can write:
\[ \text{Weight of iceberg} = \text{Weight of water displaced} \]

This can be expressed mathematically as:
\[ V \cdot \rho_{\text{ice}} \cdot g = V_1 \cdot \rho_{\text{water}} \cdot g \]

Where \( g \) is the acceleration due to gravity, which cancels out from both sides:
\[ V \cdot \rho_{\text{ice}} = V_1 \cdot \rho_{\text{water}} \]

### Step 4: Relate Submerged Volume to Total Volume
From the equation above, we can express \( V_1 \):
\[ V_1 = \frac{V \cdot \rho_{\text{ice}}}{\rho_{\text{water}}} \]

### Step 5: Substitute Known Densities
Substituting the known densities:
\[ V_1 = \frac{V \cdot 900}{1000} = 0.9V \]

### Step 6: Find Volume Above Water
Now, we can find \( V_2 \):
\[ V_2 = V - V_1 \]
\[ V_2 = V - 0.9V = 0.1V \]

### Step 7: Calculate the Percentage of Volume Above Water
To find the percentage of the iceberg's volume that is above the water, we can express it as:
\[ \text{Percentage of } V_2 = \left( \frac{V_2}{V} \right) \times 100\% \]
\[ \text{Percentage of } V_2 = \left( \frac{0.1V}{V} \right) \times 100\% = 10\% \]

### Conclusion
Thus, the percentage of the volume of the iceberg that is outside the water is **10%**.