When a wooden box floats in a tank of water, it displaces its own weight of water, maintaining the overall pressure below it. According to Archimedes' principle, the total weight of the water plus the box remains constant at any given depth. However, if the box is large enough to significantly raise the water level, the pressure below the box will increase due to the additional height of the water column. This increase in pressure can be calculated using the formula (density * g * h), where h is the height of the water above the point of measurement. The discussion confirms that the presence of a large box does affect the pressure in the tank.