The level of water will (2) fall.
as the surface area between the block and water will increase, the pressure on water will decrease so the level of water will also decrease.

Introduction:
When a rectangular block is placed in water, it displaces the water equal to its own volume. This displacement of water creates an upward buoyant force, which determines whether the block will float or sink. In this scenario, we have a rectangular block with dimensions of 10cm × 10cm × 15cm, and we need to analyze its behavior when floating in water with different orientations.

Analysis:
To understand the behavior of the block when floating with different sides vertical, we need to consider the principle of buoyancy and the concept of the center of mass.

Buoyancy Principle:
The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. If the buoyant force is greater than or equal to the weight of the object, it will float. If the buoyant force is less than the weight of the object, it will sink.

Center of Mass:
The center of mass of an object is the point where its mass can be considered to be concentrated. When a block is floating, the center of mass is located at the same height as the water level.

Orientation 1: 10cm Side Vertical:
In this orientation, the block is floating with its 10cm side vertical. The volume of the block is equal to the product of its dimensions: 10cm × 10cm × 15cm = 1500cm³. The block displaces 1500cm³ of water, creating an upward buoyant force equal to the weight of this displaced water.

Orientation 2: 15cm Side Vertical:
In this orientation, the block is floating with its 15cm side vertical. The volume of the block is again 1500cm³. However, the block now displaces a different volume of water, equal to its own volume when fully submerged. This means the block displaces 1500cm³ of water again.

Conclusion:
Since the block displaces the same volume of water in both orientations, the buoyant force acting on it remains the same. Therefore, the block will float at the same level in water, regardless of its orientation. The answer is option 3) The water level will remain the same. The change in orientation does not affect the buoyant force or the displacement of water, as both are determined solely by the volume of the block.