An iron casting containing a number of cavities weighs 6000 N in air and 4200 N in water. What is the total cavity volume in the casting? The density of solid iron is 7.87 g/`cm^(3)`

Explanation

To solve the problem, we need to determine the total volume of the cavities in the iron casting using the given weights in air and water, along with the density of solid iron.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Weight of the casting in air (W_air) = 6000 N
- Weight of the casting in water (W_water) = 4200 N
- Density of solid iron (ρ_iron) = 7.87 g/cm³ = 7870 kg/m³ (conversion from g/cm³ to kg/m³)
...