My Seventeenth Problem

When the cube is submerged, the water level is at height $H$ above the container base. The relationship between the liquid volume and the cube volume is:

$1 \, \text{m}^3 = 1 \, \text{m}^2 \times H - \Big (\frac{1}{2} \, m \Big )^3 \\ \implies H = \frac{9}{8} \, \text{m}$

The distance from the bottom of the cube to the base of the container is:

$d = H - \frac{1}{2} \, \text{m} = \frac{9}{8} \, \text{m} - \frac{1}{2} \, \text{m} = \frac{5}{8} \, \text{m} = 62.5 \, \text{cm}$