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 - axis and `15 xx 10^(6) //^(@)C` along Z axis . If the coefficient of volume expansion of the solid is `C xx 10^(-6)//^(@)C` then the value of C is ____.

Explanation

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

### Step 1: Understand the Coefficients of Linear Expansion
We are given the coefficients of linear expansion along the three axes:
- \( \alpha_x = 5 \times 10^{-5} \, /^{\circ}C \) (along x-axis)
- \( \alpha_y = 5 \times 10^{-6} \, /^{\circ}C \) (along y-axis)
- \( \alpha_z = 15 \times 10^{-6} \, /^{\circ}C \) (along z-axis)

### Step 2: Use the Formula for Volume Expansion
The coefficient of volume expansion \( \beta \) can be calculated using the formula:
\[ \beta = \alpha_x + \alpha_y + \alpha_z \]

### Step 3: Substitute the Values
Now, substituting the given values into the formula:
\[ \beta = (5 \times 10^{-5}) + (5 \times 10^{-6}) + (15 \times 10^{-6}) \]

### Step 4: Convert to Common Units
To add these coefficients, we need to express them in the same unit. The first term is already in \( 10^{-5} \), so we can convert the others:
- \( 5 \times 10^{-6} = 0.5 \times 10^{-5} \)
- \( 15 \times 10^{-6} = 1.5 \times 10^{-5} \)

Now we can rewrite the equation:
\[ \beta = (5 \times 10^{-5}) + (0.5 \times 10^{-5}) + (1.5 \times 10^{-5}) \]

### Step 5: Perform the Addition
Now, adding these values together:
\[ \beta = 5 + 0.5 + 1.5 = 7 \times 10^{-5} \]

### Step 6: Express in Required Form
We need to express \( \beta \) in the form \( C \times 10^{-6} \):
\[ \beta = 70 \times 10^{-6} \, /^{\circ}C \]

### Conclusion
Thus, the value of \( C \) is:
\[ \boxed{70} \]