A cube of ice of edge 4 cm is placed in an empty cylindrical glass of inner diameter 6 cm. Assume that the ice melts uniformly from each side so that it always retains its cubical shape. Remembering that ice is lighter than water, find the length (in cm) of the edge of the ice at the instant it just leaves the contact with the bottom of the glass.

Explanation

To solve the problem, we need to find the edge length of the ice cube at the moment it just leaves contact with the bottom of the cylindrical glass. We will use the principles of buoyancy and the relationship between the densities of ice and water.

### Step-by-Step Solution:

1. **Initial Setup**:
- The edge length of the initial cube of ice, \( L_0 = 4 \, \text{cm} \).
- The volume of the ice cube, \( V_{\text{ice}} = L_0^3 = 4^3 = 64 \, \text{cm}^3 \).
- The inner diameter of the glass is \( 6 \, \text{cm} \), so the radius \( r = \frac{6}{2} = 3 \, \text{cm} \).
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