A non-isotropic solid metal cube has coefficients of linear expansion as` 5 xx 10^(–5) //''^(@)C` along the x-axis and` 5 xx 10^(–6)//""^(@)C `along the y and the z-axis. If coefficient of volume expansion of the solid is `C xx 10^(–6) //""^(@)C` then the value of C is

Answer

To find the coefficient of volume expansion \( C \) for the given non-isotropic solid metal cube, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Coefficients of Linear Expansion**:
- The coefficient of linear expansion along the x-axis is given as:
\[ \alpha_x = 5 \times 10^{-5} \, \text{°C}^{-1} \]
- The coefficient of linear expansion along the y-axis and z-axis is:
\[ \alpha_y = \alpha_z = 5 \times 10^{-6} \, \text{°C}^{-1} \]

2. **Use the Formula for Coefficient of Volume Expansion**:
- The coefficient of volume expansion \( \beta \) is related to the coefficients of linear expansion by the formula:
\[ \beta = \alpha_x + \alpha_y + \alpha_z \]

3. **Substitute the Values**:
- Substitute the values of \( \alpha_x \), \( \alpha_y \), and \( \alpha_z \) into the formula:
\[ \beta = 5 \times 10^{-5} + 5 \times 10^{-6} + 5 \times 10^{-6} \]

4. **Calculate the Sum**:
- First, convert \( 5 \times 10^{-5} \) to the same power of ten as \( 5 \times 10^{-6} \):
\[ 5 \times 10^{-5} = 50 \times 10^{-6} \]
- Now, add the values:
\[ \beta = 50 \times 10^{-6} + 5 \times 10^{-6} + 5 \times 10^{-6} = 50 \times 10^{-6} + 10 \times 10^{-6} = 60 \times 10^{-6} \]

5. **Identify the Value of \( C \)**:
- The coefficient of volume expansion is given in the form \( C \times 10^{-6} \). From our calculation, we have:
\[ \beta = 60 \times 10^{-6} \]
- Therefore, comparing both expressions:
\[ C = 60 \]

### Final Answer:
The value of \( C \) is \( \boxed{60} \).