We have a vessel in shape of a cuboid partially filled with water. Its base is square with an area of $4.5\ {dm}^{2} (1\ dm = 10\ cm)$ and the vessel contains water up to $2\ cm$ height. Then we place a wooden cube inside water. The wood has mass of $4\ kg$ and specific gravity $0.5$. The base of the wooden cube is horizontal. Find the height of water level above the base of the wooden block.

The 4 kg wooden block has a specific gravity of 0.5, meaning its total volume is 4000 g divided by 0.5 g/cm^3, which equals 8000 cm^3 and gives a cube base side length of 20 cm. To float, the block must displace a volume of water equal to its own mass, requiring 4000 cm^3 of submerged volume. The submerged volume is also equal to the base area of the block multiplied by the water height, so 400 cm^2 times the height equals 4000 cm^3, making the water height 10 cm.

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