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When an object floats in water, the weight of water that is displaced by the block of wood is equal to the weight of the wooden block.

Weight of the wooden block acts downwards. The force of buoyancy by water on the wooden block acts upwards. They are equal and in opposite directions.

Since weight = mass * g (acceleration due to gravity = 9.8m/sec²), the mass of water displaced and mass of wooden block are same.

Mass of block of wood = 40 cm * 15 cm² * density = 600*density   grams

Amount of water displaced by wooden block
          = volume of wooden block immersed in water
         = (1 - 3/8) * 40 * 15 cm³ = 375 cm³

Mass of the amount of water displaced = 375 cm³ * 1 gm/cm³  = 375 grams

600 density = 375

Density = 375 /600 = 3/8 = 0.625 gm/cm³

(Density = fraction of length or height immersed in water)