An iron casting has a number of cavities in it. It weighs `6000 N` in air and `4000 N` in water. Determine the total volume of all the cavities in the casting. The density of iron (without cavities) is `8.0 g//cm^(3), rho_(w)= I g//cm^(3)`.

Explanation

To solve the problem, we need to determine the total volume of all the cavities in the iron casting. We will use the given weights in air and water, along with the densities of iron and water.

### Step-by-step Solution:

1. **Identify the Given Values:**
- Weight of the casting in air, \( W = 6000 \, \text{N} \)
- Weight of the casting in water, \( W_{\text{effective}} = 4000 \, \text{N} \)
- Density of iron, \( \rho_{\text{iron}} = 8.0 \, \text{g/cm}^3 = 8000 \, \text{kg/m}^3 \)
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