An inflatable device with a density of 1.20 g/`cm^(3)` is fully submerged in fresh water and then inflated enough for the device's density to match that of the water. What then is the ratio of the expanded volume to the full volume of the device?

Explanation

To solve the problem, we need to find the ratio of the expanded volume to the full volume of the inflatable device when its density matches that of fresh water. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the initial conditions
The inflatable device has a density of \( \rho_d = 1.20 \, \text{g/cm}^3 \). When fully submerged in fresh water, the density of fresh water is \( \rho_w = 1.00 \, \text{g/cm}^3 \).

### Step 2: Define the mass and volume of the device
Let the volume of the device be \( V \) and its mass be \( m \). The density of the device can be expressed as:
\[
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