When the temperature of a copper coin is raised by `80^@C`, its diameter increases by `0.2%`.

Options

A. Percentage rise in the area of a face is 0. `4%`
B. Percentage rise in the thickness is 0.4%
C. Percentage rise in the volume is `0.6%`
D. Coefficient of linear expansion of copper is `0.25xx10^(-4)//^(@)C`

Explanation

To solve the problem, we need to determine the linear expansion coefficient of copper based on the given information about the change in diameter of a copper coin when its temperature is raised.

### Step-by-Step Solution:

1. **Identify Given Information:**
- Change in temperature (ΔT) = 80°C
- Percentage increase in diameter = 0.2%

2. **Convert Percentage Increase to Decimal:**
- The percentage increase in diameter can be expressed as a decimal:
\[ \text{Increase in diameter} = \frac{0.2}{100} = 0.002 \]

3. **Use the Formula for Linear Expansion Coefficient (α):**
- The linear expansion coefficient (α) is given by the formula:
\[ \alpha = \frac{\Delta L / L_0}{\Delta T} \]
- Here, ΔL is the change in length (or diameter in this case), L_0 is the original length (or diameter), and ΔT is the change in temperature.

4. **Substituting the Values:**
- We can substitute the values into the formula:
\[ \alpha = \frac{0.002}{80} \]

5. **Calculate α:**
- Performing the calculation:
\[ \alpha = \frac{0.002}{80} = 2.5 \times 10^{-5} \, \text{°C}^{-1} \]

6. **Interpret the Results:**
- The calculated linear expansion coefficient indicates how much the material expands per degree Celsius of temperature increase.

7. **Determine the Effects on Area and Volume:**
- The increase in area (A) due to linear expansion is given by:
\[ \text{Percentage increase in area} = 2 \times \text{Percentage increase in diameter} = 2 \times 0.2\% = 0.4\% \]
- The increase in volume (V) is given by:
\[ \text{Percentage increase in volume} = 3 \times \text{Percentage increase in diameter} = 3 \times 0.2\% = 0.6\% \]

8. **Conclusion:**
- The increase in diameter is 0.2%, the increase in area is 0.4%, and the increase in volume is 0.6%. Therefore, the correct options based on the increase in area and volume are A, C, and D.