Statement-1: An ice cube is floating in water in a vessel at `0^(@)C` when ice cube melts level of water in the vessel remain same.
Statement-2: Volume of melted ice is same as volume of water displaced by ice.

Options

A. Statement-1, is true, Statement-2 is true, Statement-2 is correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is NOT a correct explantion for statement-1
C. statement-1 is true, statement-2 is false
D. statement-1 is false statement-2 is false

Answer

To solve the question, we need to analyze both statements provided:

**Statement-1:** An ice cube is floating in water in a vessel at 0°C. When the ice cube melts, the level of water in the vessel remains the same.

**Statement-2:** The volume of melted ice is the same as the volume of water displaced by the ice.

### Step-by-Step Solution:

1. **Understanding the Situation:**
- An ice cube is floating in water. According to Archimedes' principle, the weight of the water displaced by the ice cube is equal to the weight of the ice cube.

2. **Analyzing Statement-1:**
- When the ice cube melts, it turns into water. The question states that the water level remains the same after the ice melts. To understand this, we need to consider the volume of the ice and the volume of the water it displaces.

3. **Analyzing Statement-2:**
- The volume of melted ice is indeed the same as the volume of water displaced by the ice. This is because the ice cube, while floating, displaces a volume of water equal to its weight. Since ice is less dense than water, it occupies a larger volume when solid than when it is melted into water.

4. **Conclusion:**
- Since the volume of the melted ice is equal to the volume of water displaced by the ice, when the ice melts, it does not change the overall water level in the vessel. Therefore, both statements are true.
- Moreover, Statement-2 provides the correct explanation for Statement-1.

### Final Answer:
Both Statement-1 and Statement-2 are true, and Statement-2 is the correct explanation for Statement-1.