# A raft is constructed of wood having a density of 508.0 kg/m^3. The surface area of the bottom of the raft is 5.4 m^2, and the volume of the raft is 0.55 m^3.When the raft is placed in fresh water...

A raft is constructed of wood having a density of 508.0 kg/m^3. The surface area of the bottom of the raft is 5.4 m^2, and the volume of the raft is 0.55 m^3.

When the raft is placed in fresh water having density 1010.3 kg/m^3, how deep is the bottom of the raft below water level?

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### 1 Answer

The raft is constructed of wood with a density 508.0 kg/m^3. And the volume of the raft is 0.55 m^3. This gives the mass of the raft as 508.0*0.55 = 279.4 kg.

When the raft is placed in fresh water with a density 1010.3 kg/m^3, it floats when the mass of the volume of water displaced is equal to the mass of the raft. Let the bottom of the raft be M m below the water level. The surface area of the bottom of the raft is 5.4 m^2. The volume of water displaced is 5.4*M

5.4*M*1010.3 = 279.4

=> M = 0.0512 m

The bottom of the raft has to be at a depth of 0.0512 m below the surface of the water for the raft to be able to float.