Use Archimedes Principle to find deep a floating block sits in the water. Given the length width and height of this block we can solve for the displacement of fluid by the block, which in turn produces a buoyant force. In order for the Net force on the block to equal zero, the force by gravity is equal to the buoyant force and the buoyant force is equal to the weight of water displaced by the block.

This problem comes up in introductory physics, fluid mechanics, and engineering courses.