A non-isotropic solid metal cube has coefficient of linear expansion as : `5xx10^(-4)//^(@)C` along x-axis and y-axis and `5xx10^(-5)//^(@)C` along z-axis. If the coefficient of volume expansion of the solid is `gammaxx10^(-5)//^(@)C` then the value of `gamma` is __________ (in `//^(@)C`)

Explanation

To find the coefficient of volume expansion \( \gamma \) for the non-isotropic solid metal cube, we can use the relationship between the linear expansion coefficients and the volume expansion coefficient.

### Step 1: Understand the Coefficients
The coefficients of linear expansion are given as:
- \( \alpha_x = \alpha_y = 5 \times 10^{-4} \, ^\circ C^{-1} \) (along x and y axes)
- \( \alpha_z = 5 \times 10^{-5} \, ^\circ C^{-1} \) (along z axis)

### Step 2: Volume Expansion Coefficient Formula
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