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MissPhiladelphia
The information needed for this question is the density of water. When we sum the forces acting on the system we would have:

Weight = Buoyant Force
mass of gold (g) = mass of H2O displaced (g)
mass of gold = density of water (Volume displaced)
Volume displaced = 18.2 g / 1000 g / L
Volume displaced = 0.0182 L or 18.2 mL

Answer: 0.942 ml

Explanation:

To calculate volume  of a substance, we use the equation:

[tex]\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}[/tex]

We are given:

Mass of gold= 18.2 g

Density of gold = [tex]19.32g/ml[/tex]

Volume of gold = volume of water displaced = ?

Putting values in above equation, we get:

[tex]19.32g/ml=\frac{18.2g}{\text{Volume of water displaced}}[/tex]

[tex]{\text{Volume of water displaced}}=0.942ml[/tex]

Hence, the volume of water, in milliliters, that would be displaced by a piece of gold weighing 18.2 g is 0.942.

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