An ice cube floats in water. What percentage of volume is outside water. Density of water `= 1g// c c`, density of ice `= 0.9 g// c c`.

Options

A. `0.04`
B. `0.4`
C. `0.96`
D. None of these

Answer

To solve the problem of determining the percentage of the volume of an ice cube that is outside of water when it floats, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Density of water, \( \rho_w = 1 \, \text{g/cm}^3 \)
- Density of ice, \( \rho_i = 0.9 \, \text{g/cm}^3 \)
- Let the total volume of the ice cube be \( V \).

2. **Understand the Concept of Buoyancy:**
- When an object floats, the weight of the object is equal to the buoyant force acting on it.
- The buoyant force is equal to the weight of the water displaced by the submerged part of the ice cube.

3. **Set Up the Equations:**
- The weight of the ice cube is given by:
\[ \text{Weight of ice} = V \cdot \rho_i \cdot g \]
- The buoyant force acting on the ice cube is given by:
\[ \text{Buoyant force} = V' \cdot \rho_w \cdot g \]
where \( V' \) is the volume of the ice cube that is submerged in water.

4. **Apply the Principle of Equilibrium:**
- At equilibrium, the weight of the ice cube equals the buoyant force:
\[ V \cdot \rho_i \cdot g = V' \cdot \rho_w \cdot g \]
- We can cancel \( g \) from both sides:
\[ V \cdot \rho_i = V' \cdot \rho_w \]

5. **Express the Submerged Volume:**
- Rearranging the equation gives:
\[ V' = \frac{V \cdot \rho_i}{\rho_w} \]
- Substituting the values of densities:
\[ V' = \frac{V \cdot 0.9}{1} = 0.9V \]

6. **Calculate the Volume Outside Water:**
- The volume of the ice cube that is outside the water is:
\[ V_{\text{outside}} = V - V' = V - 0.9V = 0.1V \]

7. **Determine the Percentage of Volume Outside Water:**
- The percentage of the volume outside the water is given by:
\[ \text{Percentage outside} = \left( \frac{V_{\text{outside}}}{V} \right) \times 100 = \left( \frac{0.1V}{V} \right) \times 100 = 10\% \]

### Final Answer:
The percentage of the volume of the ice cube that is outside of the water is **10%**.