Final answer:
The volume of the wood block is 28 cm³. This calculation is based on the principles of density and buoyancy, which dictate that the combined volume of the wood and attached metal piece must equal the volume of water they displace when floating.
Step-by-step explanation:
The question involves finding the volume of the wood based on its density and the principle of buoyancy. When the wood block, combined with a metal piece, barely floats in water, it means the combined densities and volumes of the wood and metal are equal to the water they displace. Density of water is 1.00 g/cm³. Given the 5 g metal piece has a volume of 2 cm³, it has a density of 2.5g/cm³. The mass of the wood and metal together is 30 g, and they must displace 30 g of water to float, which is a volume of 30 cm³. Subtracting the metal's volume from the total volume will give us the wood's volume.
Volume of water displaced = mass of wood and metal = 30 g. Hence, Volume of wood and metal together = 30 cm³. Subtracting the metal volume from the combined volume gives: Volume of wood = 30 cm³ - 2 cm³ = 28 cm³.