The base of a tub is square with sides of length 1 meter. It contains water 3 centimeters deep. A heavy rectangular block is placed in the tub three times. Each time, the face that rests on the bottom of the tub has a different area. When this is done, the water in the tub ends up being 4 centimeters, 5 centimeters, and 6 centimeters deep. Find the dimensions of the block.
Source: AHSMC