Statement-`1`: A sphere, a cube and a thin circular plate made of same material and of same mass are initially heated to `200^(@)C`,the plate will cool at fastest rate.
Statement-`2`: Rate of cooling =`(rhoAsigma)/(ms)(T^(4) - T_(0)^(4))alpha "surface area"`. Surface area is maximum for circularplate.

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 correct explanation for Statement - `1`
C. Statement -`1` is True , Statement -`2` is False.
D. Statement -`1` is False , Statement -`2` is True.

Answer

To solve the problem, we need to analyze the two statements provided and determine their validity based on the principles of cooling and surface area.

### Step-by-Step Solution:

1. **Understanding the Statements**:
- **Statement 1**: A sphere, a cube, and a thin circular plate made of the same material and of the same mass are initially heated to 200°C. The plate will cool at the fastest rate.
- **Statement 2**: The rate of cooling is given by the formula \( \frac{\rho A \sigma}{m_s} (T^4 - T_0^4) \), which indicates that the rate of cooling is proportional to the surface area \( A \).

2. **Analyzing Statement 1**:
- The cooling rate of an object is influenced by its surface area. The greater the surface area, the more heat can be lost to the environment, leading to a faster cooling rate.
- Among the sphere, cube, and thin circular plate, we need to compare their surface areas.

3. **Calculating Surface Areas**:
- **Sphere**: The surface area \( A_s \) of a sphere is given by \( 4\pi r^2 \).
- **Cube**: The surface area \( A_c \) of a cube with side length \( a \) is given by \( 6a^2 \).
- **Thin Circular Plate**: The surface area \( A_p \) of a circular plate with radius \( r \) is given by \( \pi r^2 \).

4. **Comparing Surface Areas**:
- For the same mass and material, the dimensions of the objects will differ. However, the thin circular plate generally has a larger surface area compared to the sphere and cube for the same mass.
- Therefore, the thin circular plate will indeed have the maximum surface area among the three shapes.

5. **Analyzing Statement 2**:
- The formula for the rate of cooling shows that it is directly proportional to the surface area \( A \). Since the circular plate has the maximum surface area, it will cool faster than the sphere and cube.

6. **Conclusion**:
- Both statements are true. Statement 2 correctly explains why the thin circular plate (Statement 1) cools at the fastest rate due to its maximum surface area.

### Final Answer:
Both statements are true, and Statement 2 is the correct explanation for Statement 1. Therefore, the answer is option A.