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. `25%`

Explanation

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

### Step 1: Understand the concept of buoyancy
When an object floats in a fluid, the weight of the fluid displaced by the object is equal to the weight of the object itself. This is known as Archimedes' principle.

### Step 2: Define variables
Let:
- \( V \) = total volume of the iceberg
- \( V_w \) = volume of the iceberg submerged in water
- \( V_{out} \) = volume of the iceberg above water (which we need to find)

From the problem, we know:
- Density of the iceberg, \( \rho_{ice} = 900 \, \text{kg/m}^3 \)
- Density of water, \( \rho_{water} = 1000 \, \text{kg/m}^3 \)

### Step 3: Set up the weight balance equation
The weight of the iceberg can be expressed as:
\[ \text{Weight of iceberg} = \rho_{ice} \cdot V \cdot g \]
where \( g \) is the acceleration due to gravity.

The weight of the water displaced is:
\[ \text{Weight of water displaced} = \rho_{water} \cdot V_w \cdot g \]

According to Archimedes' principle:
\[ \text{Weight of iceberg} = \text{Weight of water displaced} \]
Thus,
\[ \rho_{ice} \cdot V \cdot g = \rho_{water} \cdot V_w \cdot g \]

### Step 4: Simplify the equation
We can cancel \( g \) from both sides:
\[ \rho_{ice} \cdot V = \rho_{water} \cdot V_w \]

### Step 5: Relate submerged volume to total volume
The volume of the iceberg submerged in water can be expressed as:
\[ V_w = V - V_{out} \]

Substituting this into the equation gives:
\[ \rho_{ice} \cdot V = \rho_{water} \cdot (V - V_{out}) \]

### Step 6: Solve for \( V_{out} \)
Rearranging the equation:
\[ \rho_{ice} \cdot V = \rho_{water} \cdot V - \rho_{water} \cdot V_{out} \]
\[ \rho_{water} \cdot V_{out} = \rho_{water} \cdot V - \rho_{ice} \cdot V \]
\[ V_{out} = V \left( \frac{\rho_{water} - \rho_{ice}}{\rho_{water}} \right) \]

### Step 7: Calculate the percentage of volume above water
The percentage of the volume of the iceberg that is above water is given by:
\[ \text{Percentage} = \left( \frac{V_{out}}{V} \right) \times 100 \]

Substituting \( V_{out} \):
\[ \text{Percentage} = \left( \frac{V \left( \frac{\rho_{water} - \rho_{ice}}{\rho_{water}} \right)}{V} \right) \times 100 \]
\[ \text{Percentage} = \left( \frac{\rho_{water} - \rho_{ice}}{\rho_{water}} \right) \times 100 \]

### Step 8: Substitute the values
Now substituting the densities:
\[ \text{Percentage} = \left( \frac{1000 - 900}{1000} \right) \times 100 \]
\[ \text{Percentage} = \left( \frac{100}{1000} \right) \times 100 \]
\[ \text{Percentage} = 10\% \]

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